Minerals Engineering 53 (2013) 48–56

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Minerals Engineering

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Formulating and optimising the compressive strength of controlledlow-strength materials containing mine tailings by mixture designand response surface methods

0892-6875/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.mineng.2013.07.007

⇑ Corresponding author. Tel.: +61 2 9385 4236; fax: +61 2 9313 7269.E-mail address: s.bouzalakos@unsw.edu.au (S. Bouzalakos).

S. Bouzalakos a,⇑, A.W.L. Dudeney b, B.K.C. Chan c

a School of Mining Engineering, Australian Centre for Sustainable Mining Practices (ACSMP), University of New South Wales, Sydney NSW 2052, Australiab Centre for Environmental Policy, Imperial College London, South Kensington Campus, London SW7 2AZ, UKc Environmental Division, Zijin Mining and Metallurgy Research Institute, Fujian 364200, China

a r t i c l e i n f o

Article history:Received 24 April 2013Accepted 9 July 2013

Keywords:Cemented waste compositesControlled low-strength materialsExperimental designUnconfined compressive strengthTailings

a b s t r a c t

Controlled low-strength materials (CLSM), like other cement-based backfill materials, are typically for-mulated by trial-and-error methods to yield the desired product characteristics. This paper presentsthe use of mixture design and response surface methods as tools to optimise formulations of CLSM toachieve desirable mechanical integrity with a minimum amount of statistically-sound experiments;while minimising the amount of cement and maximising the amount of by-products used. Statisticalcombinations of three-component mixtures were formulated to investigate the unconfined compressivestrength (UCS) of CLSM comprising: Portland cement, fly ash and mine flotation tailings from a Ni–Cu ore.The data is analysed using the response surface method (using a mixture design of a constrained trian-gular surface) and ANOVA. Optimum formulations are simulated using a desirability function set at lower(1.0 MPa), target (2.0 MPa) and upper (3.0 MPa) UCS values after 28 days curing. All mix combinationshad a constant spread diameter of 229 ± 10 mm, the standard workability for conventional CLSM. Resultsare compared to conventional CLSM incorporating silica sand in the place of the tailings. A significantquantity of tailings (up to 80 wt% solids) and low quantity of cement (up to 5 wt% solids) produced CLSMwith UCS within the 2 MPa target value of excavatability. UCS of CLSM is a function of the individual com-ponent proportions, and the mixture design approach can be an important tool to help develop and opti-mise formulations of cement-based materials consisting of several components.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Mine backfill and CLSM

Mineral industry waste is normally discarded, at significantcost, to dumps (coarse material) and tailing dams (fine material).The cost and liability of surface storage facilities are increasing,mainly owing to stringent environmental regulation and mine clo-sure requirements, gradually transforming the economics of minewaste disposal. Efficient management reduces disposal as far aspossible, particularly by re-use of mineral matter in backfill ofmining voids and in civil engineering works (Dudeney et al.,2013; Lottermoser, 2010).

Mine tailings have been successfully applied in hydraulic back-fill, e.g., Sivakugan et al. (2006), and more recently as cementedpaste backfill, e.g., Benzaazoua et al. (2006), to underground andsurface mining voids. The use of controlled low-strength materials

(CLSM), otherwise known as ‘flowable fill’, in the constructionindustry has increased dramatically in many countries over thepast two decades (Trejo et al., 2004). CLSM have not been exten-sively applied in the mining industry but might find increasingapplication as an alternative backfill with mineral waste or incomplementary construction works in the minerals projects, e.g.,Dudeney et al. (2013), Chan et al. (2009, 2008) and Bouzalakoset al. (2008).

CLSM are typically amalgamations of Portland cement (PC), flyash (FA), fine and/or coarse aggregates, e.g., sand and/or by-prod-ucts from various industrial processes, and water; that uponhydration of the cementitious and pozzolanic material producesa solidified geotechnical composite suitable for low load-bearingfill applications. CLSM are credited with several advantages overconventional backfill, applicable to both surface and undergroundoperations. These advantages include reduced costs arising fromthe elimination of the need for separate levelling and compaction,faster emplacement and ability to place material efficiently in con-fined spaces. The use of by-products could also reduce the demandon landfills. They have similarities to cemented paste backfill and

Table 1Physical properties of materials used in CLSM formulations.

Parameter FA SS PC T

Water content (wt%) 14.0 – – 1.00pH (slurry) 10.2 7.10 12.6 6.74Specific gravity 1.96 2.37 2.77 2.72BET surface area (m2/g) 2.65 1.00 1.10 30.2Mean particle size (lm) 31.2 250 10.1 29.1Median particle size (lm) 21.1 380 15.8 17.5% Fines (<20 lm) 48.5 – 56.7 53.8LOI (wt%) 6.00 – 1.20 11.4

S. Bouzalakos et al. / Minerals Engineering 53 (2013) 48–56 49

might suit similar or complementary applications (Ouellet et al.,2007). Important differences are recognised between the two typesof fill material, particularly in consistency, i.e., the workability ofthe fresh mix. Thus, CLSM are free-flowing slurries prior to settingwhile paste backfill with mine waste is viscous and requires acostly pumping system to drive the material to underground minevoids. Expensive de-watering is also required to pre-thicken thetailings (Henderson and Revell, 2005).

According to the American Concrete Institute (ACI) Committee229, CLSM usually have a compressive strength of 8.3 MPa or less;although they are often proportioned to develop strengths muchless than the limit (ACI Committee 229, 2006). Gabr and Bowders(2000) recommend that if the mixture is intended to be removedat a later date the maximum design strength should be around2.0 MPa after 28 days of curing in order to be excavatable bymechanical equipment such as backhoes. This is in agreement withAdaska (1997) who states that CLSM may have a 28 day compres-sive strength of 1.0–1.4 MPa, or in the case of CLSM with fine sandor fly ash as the only aggregate filler may be excavated with a back-hoe at strengths up to 2.0 MPa. Similarly, CLSM with mineral wastein Chan et al. (2009) and Bouzalakos et al. (2008) gave 28 day com-pressive strengths predominantly <2.0 MPa. Workability is anotherimportant property of CLSM. The ACI recommends CLSM shouldproduce a spread diameter of 200–300 mm, with conventional lab-oratory-scale CLSM being in the region of 229 ± 10 mm. Bleedingshould be kept under 2% for an acceptable amount of consolidation(ACI Committee 229, 2006).

1.2. Proportioning of CLSM

There are no statistics-based guidelines available on the propor-tioning of CLSM. The majority of compositional studies, regardingmost cement-based materials, have focused on traditional experi-mental design methodologies with two or more factors, i.e., inde-pendent variables, such as the one-factor-at-a-time (OFAT)approach (e.g., Yeh, 2006; Mac Berthouex and Brown, 2002). Inthese cases, one component is varied at a time and all others arekept constant. This process is repeated by varying other compo-nents one by one until all the components have been tested. Suchtechniques usually require a great number of experiments to yieldthe desired product characteristics that are often not satisfactorybecause of interactions between components (Yeh, 2006). More-over, it is common that industrial experimenters initially turn totwo-level factorial designs consisting of all combinations of eachfactor at its high and low levels to produce estimates of the maineffects and interactions. However, when the response depends onthe proportions of ingredients, i.e., dependent variables, such asthe compressive strength of cement-based materials, the factorialdesign approach is not suitable as it depends on independent vari-ables (Yeh, 2006; Lundstedt et al., 1998).

The mixture design approach accounts for the dependence of aresponse on the proportionality of ingredients and not on theirabsolute values as would be the case in a factorial design (Lund-stedt et al., 1998). As such, these proportions are dependent vari-ables (Cornell, 2002). A mixture design experiment is a specialtype of response surface methodology in which the factors arethe components of the mixture and the response is a function ofthe proportions of each component. For a mixture experiment,the sum of the component fractions must be equal to unity andtheir proportions must be non-negative (Khuri and Cornell, 1996).

There are many industrial and research problems where theresponse variables of interest in the product are a function of theproportions of the different ingredients used in its formulation(Yeh, 2006). For example, the mixture design approach has beensuccessfully used in civil engineering materials for the optimisa-tion of formulations of: ground waste glass blended cement

(Khmiri et al., 2012); rubberised concrete (Vieira et al., 2010); con-crete (Yeh, 2006); binders for stabilisation/solidification of a phos-phogypsum by-product (Guo et al., 2003); binders for soilstabilisation (Lindh, 2001); pozzolan-based products (Nardi andHotza, 2003); and thermoplastic road markings (Mirabedini et al.,2012). The application of the mixture design methodology hasnot been previously considered for CLSM.

Fall et al. (2008) agree with other researchers in that fillingcosts for a mine typically represent in the vicinity of 20% of all min-ing costs, with cement costs constituting approximately 75% ofthat amount. Thus, any cost optimisation of backfill technologywould involve reducing the binder proportion without affectingthe strength of the material (Tariq and Nehdi, 2007). This paperpresents the use of mixture design and response surface methodsas tools to formulate and optimise formulations of CLSM to achieveUCS within the excavatable limit of 2.0 MPa with a minimumamount of statistically-sound experiments. Emphasis is given tomix designs with a minimum quantity of cement and maximumquantity of tailings used. For comparison purposes, CLSM contain-ing ordinary sand in the place of tailings have also been included.

2. Materials and methods

2.1. Materials

The materials used include binders, tailings, silica sand andwater.

2.1.1. BindersA commercially available Portland cement (PC) (Blue Circle

CEM-I, Lafarge, UK) and a low-calcium (2.57 wt% CaO), Class F, flyash (FA) (Drax Power Ltd., North Yorkshire, UK) were used asbinders in the CLSM formulations. Their physical properties areshown in Table 1. A low-calcium FA has been selected to minimiselong-term strength development of CLSM specimens (in additionto controlling bleeding). Drax is also the largest power station inthe UK and Western Europe (’4000 MW) producing great amountsof fly ash each year (’1.5 Mt/yr). Although a large proportion of flyash is sold to the construction industry, the remaining low-gradeFA is disposed in regulated mounds. Given the proportion of thismaterial, finding potential use in CLSM as a fill material in theminerals industry could provide a further sustainable option forDrax FA use. Physical properties of FA are within typical valuesof UK fly ash (Sear, 2001), although specific gravity is within thelower end of the range given a high LOI of 6 wt%. Water contentwas recorded at 14 wt% representing the standard ‘conditioning’practice with water at the power station before disposal. FA wasdried in an oven at 105 ± 5 �C for 24 h (or until no further weightreduction) prior to use in CLSM specimen preparation. The chemi-cal composition of PC and elemental analysis of FA are given inTables 2 and 3, respectively. XRD data for FA and PC are presentedin Fig. 1. It is clearly seen that the majority of crystalline phasespresent were mullite [3Al2O3�2SiO2] and quartz [SiO2] for FA, and

Table 2Chemical composition of PC.

SiO2 Al2O3 Fe2O3 CaO MgO Na2O K2O TiO2 Mn2O3 P2O5 SO3 SUM

PC (wt%) 23.6 4.24 2.40 61.6 2.59 0.27 0.88 0.32 0.06 0.32 1.37 97.65

Table 3Elemental analysis of waste materialsa.

Element (mg/g) T FA

Ag 0.000160 0.0000400Al 29.8 25.9As 0.0146 0.0594Ba 0.104 0.313Be 0.000350 0.00363Ca 29.0 18.4Cd 0.000170 0.000760Co 0.0376 0.0188Cr 0.0651 0.0405Cu 0.387 0.0654Fe 38.9 27.5K 2.75 2.84La 0.00737 0.0338Li 0.0165 0.0591Mg 24.7 4.79Mn 0.412 0.174Mo 0.000200 0.0116Na 3.00 2.45Ni 1.28 0.0567P 0.273 2.16Pb 0.00800 0.0372S 8.05 1.77Si 115 510Sr 0.111 0.682Ti 1.54 0.850V 0.0182 0.0737Zn 0.0175 0.0575

a Digestion with HNO3, HClO4 and HCl according to Thompson and Wood (1982).

Fig. 1. XRD patterns of PC and FA (A – alite, C3S; Al – tricalcium aluminate, C3A; B –belite, C2S; M – mullite, 3Al2O3�2SiO2; Pg – periclase, MgO; Q – quartz, SiO2).

Fig. 2. XRD pattern of T (Act – actinolite, Ca2(Mg,Fe)5Si8O22(OH)2; Ab – albite,NaAlSi3O8; Clc – clinochlore, (Mg,Fe,Al)6(Si,Al)4O10(OH)8; Di – diopside, CaMgSi2O6;Ms. – muscovite, KAl2(AlSi3O10)(F,OH)2).

50 S. Bouzalakos et al. / Minerals Engineering 53 (2013) 48–56

alite [C3S], belite [C2S] and tricalcium aluminate [C3A] for PC. Thepresence of amorphous material in FA is denoted by the presenceof a wide peak between 15� and 35� 2h.

2.1.2. TailingsTailings (T) derived from the flotation of a Ni–Cu ore were

obtained from the Aguablanca mine in south-western Spain. Flota-tion tailings typically have angular irregularly-shaped particles as aresult of mineral processing. The physical properties are shown in

Table 1. The fines (<20 lm) content of T was significantly higherthan the minimum threshold of ca. 15–20% for backfill materials(Henderson and Revell, 2005). T was dried in an oven at105 ± 5 �C for 24 h (or until no further mass reduction) prior touse in CLSM specimen preparation. The elemental analysis inTable 3 suggests that the tailings are characterised by a relativelyhigh amount of Si (115 mg/g) and noticeable amounts of Fe(38.9 mg/g), Al (29.8 mg/g), Ca (29.0 mg/g), Mg (24.7 mg/g) and S(8.05 mg/g). Only small amounts of heavy elements such as As(0.0146 mg/g), Cu (0.387 mg/g), Pb (0.00800 mg/g) and Zn(0.0175 mg/g) were detectable. The XRD pattern shown in Fig. 2identified a range of silicate minerals, i.e., actinolite (amphibole)[Ca2(Mg,Fe)5Si8O22(OH)2]; albite (feldspar) [NaAlSi3O8]; clinochlore(chlorite) [(Mg,Fe,Al)6(Si,Al)4O10(OH)8]; diopside (pyroxene) [CaM-gSi2O6] and muscovite (mica) [KAl2(AlSi3O10)(F,OH)2], originatingfrom the parent rock of the extracted ore that was processed. Theidentification of phyllosilicates, e.g., micas and chlorites, couldpotentially explain the high BET surface area of T in comparisonto other raw materials listed in Table 1 owing to their flake-likemineral structure.

2.1.3. Silica sandSilica sand (SS) was used as an inert, bulk mineral component in

the conventional CLSM formulations for comparison purposes. Thephysical properties are shown in Table 1. The particle size of silicasand suggests it may be classified in the medium sand range (200–600 lm).

2.1.4. WaterDe-ionised water was used for all mix formulations tested, and

favoured over tap water as a control measure to minimise anypotential reactions of tap water constituents with UCSdevelopment.

Table 4Three-component CLSM formulations.

Mix PC(wt%)

FA(wt%)

SS or T(wt%)

Density – CLSMSSa

(g/cm3)Density – CLSMT

b

(g/cm3)

1 5 10 85 2.35 2.652 5 15 80 2.33 2.613 5 20 75 2.31 2.574 8.33 13.33 78.33 2.35 2.625 10 10 80 2.37 2.656 10 15 75 2.35 2.617 15 10 75 2.39 2.65

S. Bouzalakos et al. / Minerals Engineering 53 (2013) 48–56 51

2.2. Mixture design formulations and response surface

Minitab (version 14.20) software was used to formulate andoptimise statistical combinations of the three-component CLSMmixtures. The various formulations were evaluated for their28 day UCS as this is a common design parameter for cement-based materials, including CLSM (ACI Committee 229, 2006).Furthermore, strength development control in CLSM for minebackfill applications would be the single most important criterionin developing mix designs to maintain structural integrity andexcavatability requirements.

The interpretation of UCS has been accomplished using simpli-fied polynomial (regression) models, which define a so-called re-sponse surface, to correlate the UCS to the proportions used. Thismakes the quantitative estimation of UCS of any formulation inthe studied system possible, without performing a large numberof experiments. Response surfaces can be used to satisfy certaincriteria, for instance, to maximise a property at the lowest costand/or the robustness of a process, that is, to ensure that it is lesssensitive to unexpected variations (Nardi et al., 2004).

The design of CLSM mixtures has been based on weight per-centage (wt%) of dry solids, so that the sum of all solids is equalto 100%. The water content for each mix design was adjusted togive a spread diameter of 229 ± 10 mm, following ASTM D6103-04, 2004. This allows all mix designs developed and tested to becomparable against each other since the workability was constant.The water content is expressed as wt% of the total CLSM mix, i.e.,solids plus water.

Conventional CLSM incorporating Portland cement, fly ash andsilica sand (abbreviated as PC–FA–SS) and CLSM with tailings,replacing the silica sand component of conventional CLSM (abbre-viated as PC–FA–T), are designated, hereafter, as three-componentCLSM mixtures. A three-component simplex-centroid mixture de-sign was used as illustrated by the ternary diagram representingthe simplex response surface in Fig. 3. Each design point representsa formulation, or mixture, of components (x1, x2, x3). The pointscentred on each side of the triangle represent 1:1 binary mixturesof the components or mixtures of their neighbouring vertex points.The centre point represents a 1:1:1 ternary mixture of the threecomponents represented at the vertices. A simplex-centroid designwas chosen as it includes the ternary mixture within the simplex,thus, enhancing the resolution and allowing for higher order poly-nomials to be analysed (Cornell, 2002).

Constraints on individual components were applied, and thecomponent proportions of CLSM were selected to vary from: 5 to15 wt% for PC (x1), 10–20 wt% for FA (x2) and 75–85 wt% for thebulk materials, i.e., SS and T (x3), as stated in Table 4. The bounds

Fig. 3. Ternary diagram of the response surface for the three-component simplex-centroid mixture design.

were selected with the aim of minimising the PC content and max-imising the bulk content, while satisfying CLSM requirements forexcavatability. The constraints introduced covered the entire sim-plex mixture-space (Fig. 3). The sum of the component proportionsadd up to 100% for all mix designs. The actual run order of theexperiments was randomised to minimise statistically significantbias, and the entire mix design was replicated three times to geta measure of the statistical error of the response. In terms of vol-ume fractions, solids density of PC–FA–SS reported in Table 4 arenot unusual for conventional CLSM. Addition of T to PC–FA–Tslightly increased solids density owing to greater BET surface areaand specific gravity which would influence water content (forworkability consistency) and UCS (see Section 3.2).

2.3. Regression models for statistical analysis of response

Linear (first-order) and quadratic (second-order) canonicalpolynomial models given by Eqs. (1) and (2), respectively, wereused for three-component, i.e., q = 3, CLSM mixtures to determinethe model that provided the best fit to the experimental data in or-der to make predictions of UCS for any mixture of components. Thepolynomial models take a canonical form because of the constraint,i.e., the sum of component proportions must equal to unity. Thelinear model is used, and is only valid, in the absence of interactioneffects between components. The quadratic model considersantagonistic (regression coefficients, b < 0) or synergic (regressioncoefficients, b > 0) binary-interaction effects for all possible pairsof components.

Linear model : EðyÞ ¼ b1x1 þ b2x2 þ b3x3 ð1Þ

Quadratic model : EðyÞ¼ b1x1þb2x2þb3x3þb12x1x2þb13x1x3þb23x2x3 ð2Þ

where E(y) is the response, i.e., UCS (MPa), x1, x2, x3 the amount ofPC, FA, SS or T (wt%) respectively, b1, b2, b3 the regression

a Mix designs with SS.b Mix designs with T.

Table 5ANOVA table for the fitting of a model that is linear in its parameters.a

Source of variation Degreesoffreedom(DF)

Sum of squares (SS) Mean squares (MS)

Regression p � 1 SSR ¼Pm

iPni

j ðy� �yÞ2 MSR = [SSR/(p � 1)]

Residual n � p SSr ¼Pm

iPni

j ðyij � yiÞ2 MSr = [SSr/(n � p)]

Lack of fit (LOF) m � p SSLOF ¼Pm

iPni

j ðyi � �yiÞ2 MSLOF = [SSLOF/(m � p)]

Pure error (PE) n � m SSPE ¼Pm

iPni

j ðyij � �yiÞ2 MSPE = [SSPE/(n �m)]

Total (T) n � 1 SST ¼Pm

iPni

j ðyij � �yÞ2

a ni = number of replicates at the ith level; m = number of distinct levels of theindependent variables; n = total number of observations; p = number of coefficients.

52 S. Bouzalakos et al. / Minerals Engineering 53 (2013) 48–56

coefficients for the linear terms and b12, b13, b23 is the regressioncoefficients for the binary-interaction terms.

2.4. Analysis of variance (ANOVA) of regression models

The ANOVA table for regression model evaluation and valida-tion is presented in Table 5. The total data variance is divided intotwo main contributions: the sum of squares explained by theregression (SSR), and the residual sum of squares (SSr). Both sum-mations are taken over all the experimental design levels, i = 1,2,. . .,m, and all the replicates performed at each level, j = 1,2,. . .,ni. SSR is a sum of squares of differences between values pre-dicted by the regression and the grand average of all the responsevalues. SSr is a sum of squares of differences or residuals betweenthe experimental values and the predicted values from the model.Large SSR and small SSr values tend to occur for models that accu-rately describe the experimental data.

The SSR/SST ratio represents the fraction of explained variationand is commonly represented as R2, i.e., the coefficient of determi-nation, which varies between 0 and 1. If pure error exists it isimpossible for R2 to equal 1. Although this coefficient is a measureof how close the model fits the data, it cannot be used to judge themodel lack-of-fit because it does not take into account the numberof degrees of freedom for model determination. A related statistic,the adjusted coefficient of determination (R2

adj), makes an adjust-ment for the varying number of degrees of freedom in the modelsbeing compared the following equation:

R2adj ¼ 1� n� 1

n� p

� �SSR

SSTð3Þ

Model quality can only be rigorously judged if the SSr is decom-posed into two contributions: the lack-of-fit and the pure errorsums of squares, SSLOF and SSPE. The latter is a sum of squares ofdifferences between all the individual experimental values andthe average of the experimental values at the same level. The SSLOF

is a sum of squares of differences between the values predicted ateach level and the average experimental value at that level. The P-value in the lack-of-fit may be used to evaluate the hypothesis thatthe current model is adequate. A small P-value, i.e., <0.05 at a 95%confidence level, indicates an inadequate model. The P-value isassociated with testing the null hypothesis that the model doesnot explain any of the variability in the response. The P-value rep-resents the probability that the F-distributed F-ratio (MSLOF/MSPE)is at least as large as shown if the null hypothesis was true, i.e.,all regression coefficients are zero.

2.5. Specimen preparation

The procedure for producing CLSM was similar to that of con-crete. The dry solids were initially mixed with a conventionalmechanical stirrer. De-ionised water was added gradually untilthe mix gave a spread diameter of 229 ± 10 mm. This is the desiredworkability recommended by the ACI for conventional CLSM (ACICommittee 229, 2006). The spread was measured using an open-

Fig. 4. (a) Examples of desirability functions; (b) desirabil

ended cylinder according to ASTM D6103-04, 2004. Further mixingwas carried out until the mix had a uniform consistency andappearance. The water content of each mix is represented by thewater-to-cement (w/c) and water-to-cementitious materials (w/cm) ratios shown in Tables 8 and 9.

The mix was poured into plastic, re-usable cylindrical mouldswith length-to-diameter dimensions 40:20 mm. Due to the flow-able nature of CLSM, no compaction or vibration was necessaryduring casting. Specimens were cast by pouring CLSM to overfillthe mould, tapping lightly on the mould, and subsequently struckoff. All mix designs were ensured to have 62% bleeding, and werethoroughly mixed before placing into molds to help control exces-sive consolidation. Specimens were allowed to harden for up to3 days in a desiccator containing water at the bottom (to provideclose to 100% relative humidity) in order to prevent shrinkageand water loss before mechanically de-moulding. To avoid spillingand water loss while curing, the base and top of each mould wascovered with a waterproof plastic paraffin film (Parafilm). Follow-ing de-moulding, specimens were cured in sealed plastic bags atroom temperature until required for testing. Despite low-strengthdesigns, and given the relatively small mould dimensions, 3 days ofcuring provided sufficient hardening time for samples to maintaintheir mechanical integrity for de-moulding.

2.6. Unconfined compressive strength

UCS was determined after 28 days of curing. The testing appara-tus was a mechanically driven loading system with two smooth,parallel platens (Wykeham Farrance Eng. Ltd.). No capping mate-rial was required as the waterproof paraffin film used to coverthe base and top of the mould during casting provided smoothends upon removal of the Parafilm. Specimens were made planarand smoothed, if necessary, on both ends by gentle abrasion withfind sand paper to minimise end effects. The UCS results reportedin Tables 8 and 9 are the average and standard deviation of thethree specimens tested for each mix. It should be noted that Mix7 exceeds the upper UCS limit for classification as CLSM, i.e.,8.3 MPa, but has been included for the completion of the statisticalanalysis and interpretation of results.

2.7. Optimisation approach

The optimisation process involved a numerical approach usingMinitab’s Response Optimiser to help identify the combination ofcomponents that jointly optimise the response. This is based ondefining a desirability function (D) that reflects the levels of theresponse in terms of minimum (zero) to maximum (one) desirabil-ity. One represents the ideal case; zero indicates that the responseis outside the desirable limits. Several types of desirability func-tions can be defined, the most common of which are shown inFig. 4a below. These functions can also be expressed mathemati-cally and have been extensively described by Derringer and Suich(1980).

According to Section 1.1, the majority of researchers have iden-tified CLSM to have 28 day UCS between 1.0 and 2.0 MPa. For this

ity function used for optimisation of CLSM mixtures.

Table 7ANOVA table for PC–FA–T.

Source of variation Degreesoffreedom(DF)

Sum ofsquares(SS)

Mean square(MS)

F-ratio P-value

Linear modelRegression 2 121.16 60.58 404.36 <0.001Residual error 18 2.70 0.15Lack-of-fit 4 2.45 0.61 34.15 <0.001Pure error 14 0.25 0.18

S. Bouzalakos et al. / Minerals Engineering 53 (2013) 48–56 53

reason, the ‘target-is-best’ desirability function was chosen to opti-mise CLSM formulations. The minimum desirability was set to1.0 MPa (for the lower bound limit) and 3.0 MPa (for the upperbound limit), with the maximum desirability set at the mid-pointtarget value of 2.0 MPa. The desirability function is illustrated inFig. 4b. The mathematical expression of this desirability functionhas been defined by Derringer and Suich (1980). The solutions sim-ulated contained combinations of components that were predictedto give a 28 day UCS within this region, therefore, ensuring that theexcavatability requirement of CLSM is met.

Total 20 123.86R2 = 0.9782 R2

adj ¼ 0:9758

Quadratic modelRegression 5 123.56 24.71 1233.72 <0.001Residual error 15 0.30 0.020Lack-of-fit 1 0.050 0.050 2.78 0.12Pure error 14 0.25 0.18Total 20 123.86

R2 = 0.9976 R2adj ¼ 0:9968

Table 828 Day experimental UCS, predicted UCS, mean water content, w/c and w/cm ratios,and density of PC–FA–SS.

Mix UCS (MPa) Water(wt%total)

w/c w/cm Freshdensity(g/cm3)

Experimental Predicted

1 1.02 ± 0.13 1.04 19.3 4.80 1.60 2.542 1.31 ± 0.12 1.23 21.0 5.32 1.33 2.543 2.43 ± 0.08 2.45 22.0 5.64 1.13 2.534 3.18 ± 0.10 3.37 23.7 3.72 1.43 2.595 4.15 ± 0.08 4.07 25.7 3.45 1.73 2.636 5.40 ± 0.20 5.32 27.5 3.79 1.52 2.627 8.68 ± 0.28 8.70 33.0 3.29 1.97 2.72

Table 928 Day experimental UCS, predicted UCS, mean water content, w/c and w/cm ratios,and density of PC–FA–T.

Mix UCS (MPa) Water(wt%total)

w/c w/cm Freshdensity(g/cm3)

Experimental Predicted

1 1.37 ± 0.08 1.38 26.3 7.15 2.38 2.912 1.77 ± 0.18 1.72 28.2 7.84 1.96 2.893 2.85 ± 0.17 2.86 30.7 8.85 1.77 2.884 3.60 ± 0.05 3.70 33.2 5.96 2.29 2.95

3. Results and discussion

3.1. Statistical analysis of regression models – ANOVA

The polynomial models defined in Section 2.3 were fitted to theexperimental data following an analysis of variance (ANOVA),which includes analyses of the lack-of-fit and the coefficients ofdetermination in order to determine the most adequate model thatrepresents the experimental data (Table 5). The ANOVA tables foreach CLSM formulation (Tables 6 and 7) represent a sequentialmodel-fitting procedure. That is, the simplest model, i.e., linear,was initially analysed and if it resulted in a significant lack-of-fita higher-order polynomial, i.e., quadratic, was tested, and so on,until a model with non-significant lack-of-fit and high coefficientsof determination was validated. Once the best-fitting model wasdetermined, an equation describing the prediction of UCS was pro-vided for CLSM designs. Furthermore, contour response surface andresponse trace plots were produced to show the effect of alteringthe composition of components on UCS (Section 3.2).

Even though for both PC–FA–SS (Table 6) and PC–FA–T (Table 7),the linear model gave high coefficients of determination, the P-va-lue was below 0.05 presenting evidence of lack-of-fit and was,therefore, rejected. The quadratic model, however, gave evengreater R2 and R2

adj values, with P-values in excess of 0.05 present-ing no evidence of lack-of-fit; this model, therefore, may be usefulfor quantitative predictions of the response. The regression P-valuefor both three-component CLSM mixtures was <0.05 indicating ahighly significant regression.

3.2. Response surface analyses

Two-dimensional contour response surface plots of the 28 dayUCS for three-component CLSM mixtures were produced in orderto help establish the desirable response values and mixture blends.

Table 6ANOVA table for PC–FA–SS.

Source of variation Degreesoffreedom(DF)

Sum ofsquares(SS)

Mean square(MS)

F-ratio P-value

Linear modelRegression 2 125.82 62.91 437.78 <0.001Residual error 18 2.59 0.14Lack-of-fit 4 2.34 0.56 22.38 <0.001Pure error 14 0.35 0.025Total 20 128.41

R2 = 0.9799 R2adj ¼ 0:9776

Quadratic modelRegression 5 127.89 25.58 747.27 <0.001Residual error 15 0.51 0.034Lack-of-fit 1 0.16 0.16 6.55 0.10Pure error 14 0.35 0.025Total 20 128.41

R2 = 0.9960 R2adj ¼ 0:9947

5 4.29 ± 0.10 4.25 35.5 5.50 2.75 3.006 5.71 ± 0.15 5.67 37.7 6.04 2.42 2.997 8.98 ± 0.16 9.00 41.7 4.76 2.86 3.07

Response trace plots (also called component effects plots) werealso produced and indicate the effect of changing each mixturecomponent while holding all other components at a constant ratio.The response is plotted while moving along an imaginary line froma reference blend, in this case the centroid mixture, to the vertex ofthe component being incremented. A steep slope or curvature in aninput variable indicates a relatively high sensitivity of response,and vice versa. Response trace plots are especially useful for CLSMmixtures with more than three components as the complete re-sponse surface cannot be visualised on a surface plot. The plotsare followed by equations derived from the regression model anal-ysis predicting the UCS of the CLSM mix designs. Furthermore, themean experimental and predicted UCS, water content, w/c and w/cm ratios have been tabulated for both mix designs.

The contour plots for the response surfaces of PC–FA–SS andPC–FA–T are shown in Fig. 5. It is noted that both of the mixtures

Fig. 5. Response surface contour plots of PC–FA–SS (left) and PC–FA–T (right).

Fig. 6. Response trace plot of PC–FA–SS.

Fig. 7. Response trace plot of PC–FA–T.

54 S. Bouzalakos et al. / Minerals Engineering 53 (2013) 48–56

give almost identical plots. This suggests that both mix formula-tions exhibit similar behaviour on varying the components. It isclearly seen that mixtures with high PC content give the highestUCS values. Mixtures with high SS values give the lowest UCS. Mix-ture combinations having UCS in the 2 MPa excavatability limit ofCLSM are located in the lower half of the response surfaces, asshown by the 2 MPa contour lines.

The response trace plots for PC–FA–SS (Fig. 6) and PC–FA–T(Fig. 7), as with the response surface contour plots, show very sim-ilar behaviour. It is clearly seen that for both CLSM formulations asthe proportion of PC increases the UCS also increases. The line forPC has a steep slope indicating a high sensitivity of response.Increasing the FA proportion only slightly increases the UCS.Increasing the SS proportion decreases UCS, giving a negatively-sloped line. The relatively straight nature of the lines indicatesinsignificant binary interaction between components (Muthuku-mar and Mohan, 2004).

The predicted equations for UCS derived from the model-fittingprocedure discussed in Section 2.4 are given by Eq. (4) for PC–FA–SS and Eq. (5) for PC–FA–T. It is noticed that the model-fittingprocedure resulted in very similar equations for both three-compo-nent CLSM formulations.

PC–FA–SS:

EðyÞ ¼ 2:94x1 þ 1:41x2 þ 0:044x3 � 0:010x1x2 � 0:032x1x3

� 0:021x2x3 ð4Þ

PC–FA–T:

EðyÞ ¼ 3:38x1 þ 1:09x2 þ 0:042x3 � 0:011x1x2 � 0:038x1x3

� 0:016x2x3 ð5Þ

Of the linear effects, the equations suggest that the positivecoefficient for PC (x1) has a constructive contribution to E(y), i.e.,UCS. FA (x2) also exhibits a positive coefficient, although to a lessermagnitude than PC and is expected to increase UCS with increasingamounts. The coefficient of SS (x3) is also positive but of low mag-nitude suggesting negligible effect on UCS. The negative coeffi-cients of the three binary interaction effects suggest antagonisticeffects on the response; however, the magnitude of these coeffi-cients is low. This suggests that there is minor interaction betweenthe components and is emphasised by the straight lines represent-ing the response surface contour plots in Fig. 5 and the responsetrace plots in Figs. 6 and 7. Varying the individual components ofthree-component CLSM mixtures seems to be more influential onUCS than the binary interaction of components.

The most notable differences between the two three-compo-nent CLSM mixtures are that when SS was replaced with T, UCSvalues slightly increased (up to 0.42 MPa) and the water require-

ment to produce the same workability increased significantly,i.e., in the order of approximately 8–10 wt% (Tables 8 and 9). Thelarger water requirement could be attributed to the greater BETsurface area of T. Despite increased water contents to maintainCLSM workability requirements, the increased UCS of PC–FA–T(in comparison to PC–FA–SS) is postulated to arise from additional

Table 10Optimisation solutions for conventional CLSM (PC–FA–SS).

Solution

1 2 3 4

PC (wt%) 5 5 5 6.9FA (wt%) 10 15 20 10SS (wt%) 85 80 75 83.1Predicted UCS (MPa) 1.04 1.23 2.45 2Desirability (D) 0.90 0.93 0.94 1

Table 11Optimisation solutions for PC–FA–T.

Solution

1 2 3 4

PC (wt%) 5 5 5 6.4FA (wt%) 20 10 15 10T (wt%) 75 85 80 83.6Predicted UCS (MPa) 2.86 1.38 1.72 2Desirability (D) 0.14 0.38 0.72 1

S. Bouzalakos et al. / Minerals Engineering 53 (2013) 48–56 55

CaO/MgO content of T minerals contributing to cementitious reac-tions and strength development. This, however, is an area forfurther investigation. As a result of the greater water requirement,w/c and w/cm ratios were greater for PC–FA–T (Table 8) than PC–FA–SS (Table 9). The w/c and w/cm ratios are in good agreementwith values reported in the literature for conventional CLSM. Thepredicted UCS derived from Eqs. (4) and (5) are in good agreementwith the experimental UCS for both CLSM mixtures.

3.3. Optimisation of CLSM formulations

The Minitab Response Optimiser provided a range of solutionsfitting to the range of the desirability function specified. Eventhough for some cases there was more than one formulation givingthe desired UCS, the formulation chosen as the optimum for eachCLSM mixture was the one that had the least amount of PC atthe highest quantity of waste. According to Fall et al. (2008), a PCproportion greater than 7 wt% would not be economically feasiblein the mining industry. This was taken into consideration whenchoosing the PC content of optimal mixtures.

The solutions derived for PC–FA–SS and PC–FA–T from the opti-misation procedure are presented in Tables 10 and 11, respectively.The highlighted column is derived as the optimum formulation. Forboth CLSM formulations 5 wt% PC, 15 wt% FA and 80 wt% of SS (orT) were selected as optimum solutions (i.e., Solution 2 for PC-FA-SSand Solution 3 for PC-FA-T) for subsequent experimentation oftheir physical, chemical and microstructural properties (Bouzala-kos, 2008). Although D – 1 for the combination of components,they were selected since in both cases a minimum amount of PCwas used (<7 wt%). Tables 10 and 11 suggest that using 20 wt%FA would increase UCS desirability, however, the amount of bulkmaterial would be 5 wt% less therefore selecting 15 wt% FA asthe optimum amount.

4. Conclusions

The employment of the mixture design methodology has beenshown to be an important tool to help develop formulations of ce-ment-based materials consisting of several components, as theirproperties are a function of the proportions of the components,rather than performing trial-and-error runs or varying the propor-tions of one component at a time.

The predicted UCS are in good agreement with the experimentalUCS and the application of optimisation techniques has enabled

the development of cost-effective CLSM, i.e., PC <7 wt%, while sat-isfying workability, i.e., spread diameter of 229 ± 10 mm, andexcavatability, i.e., UCS 62.0 MPa, requirements for classificationas CLSM and maximising waste content used. Model validationusing ANOVA analyses, lack-of-fit tests and coefficients of determi-nation confirms that the optimum formulations chosen are reliableand accurate.

Valuable results have been gained regarding the interactionsbetween components and their effect on UCS. As expected, PC sig-nificantly influenced UCS of both CLSM designs. FA also positivelyinfluenced UCS but to a lesser extent. The three-component CLSMmixtures evaluated did not show significant blending interactionbetween components suggesting that individual components havea greater effect on UCS than their combination. Optimised watercontents were similar to trial-and-error values reported in the lit-erature. The addition of tailings (T) significantly increased waterdemand and slightly increased UCS. This effect is likely to be a re-sult of relatively significant levels of CaO (and to a lesser extentmagnesium) and the phyllosilicate minerals comprising T contrib-uting to the hydration reactions of the cementitious materials, i.e.,PC and FA.

In order for mixture design and response surface methodologiespresented herein to substantiate a degree of generic character foroptimising mechanical (and a combination of other, e.g., hydro-lytic) properties of CLSM, further work is necessary to test a widerrange of mineral waste streams, and formulating mixture designswith more than three components.

Acknowledgements

This work was carried out in the frame of BioMinE (Europeanproject contract NMP1-CT-500329-1). The authors acknowledgethe financial support given to this project by the European Com-mission under the Sixth Framework Programme for Research andDevelopment. Thanks are due to the Natural History Museum, Lon-don; B.K.C. Chan; B.J. Coles; M.G. Gill and G. Nash for contributionsto experimental procedures and/or results. They also extend theirthanks to Río Narcea Recursos, S.A. (Spain), Técnicas Reunidas,S.A. (Spain) and Drax Power Ltd. (UK) for the supply of materials.

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