Mix proportioning of underground cemented tailings backfill

M. Fall a,*, M. Benzaazoua b, E.G. Saa c

a Department of Civil Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, Ont., Canada K1N 6K7b University of Quebec in Abitibi-Temiscamingue (UQAT), Rouyn-Noranda, Que., Canada, J9X 5E4

c Ecole Polytechnique Federale de Lausane, Switzerland

Received 27 August 2005; received in revised form 6 August 2006; accepted 12 August 2006

Available online 20 February 2007

Abstract

The usage of cemented tailings backfill (cemented paste backfill) in the underground by mining industry is becoming increasinglyimportant. However, until now, the mix proportioning of CTB has been mainly based on the realization of extensive laboratory testson a large number of CTB mixes. Therefore, this paper presents a design method for mix proportioning of CTB to minimize the numberof trial mixes and provide an appropriate mix proportion. This method is based on the pairing of the response surface method (RSM)and the desirability approach. First, the RSM was used to develop predictive models for the performance properties of CTB. The pre-dicted properties in question are the uniaxial compression strength (UCS), the slump, the solid concentration (solid percent, %Solid) andthe cost (based on cement cost) of the CTB. The predictive models that were developed were able to accurately represent the relationshipsbetween the physical and chemical characteristics of the CTB components (tailings, binder, water) and the above properties. The resultsof the modeling phase were then used as input data in the optimization phase (based on desirability approach) to develop optimal recipesfor the studied CTBs. This study has demonstrated that the combination of the RSM and desirability approach represents an effectivetool for CTB mix proportioning. It has also shown that the mix parameters (cement content, water-to-cement ratio, tailings fineness anddensity) affect the performance properties of CTB. The results of this research provide a more comprehensive engineering approach toCTB mix proportioning. The developed design method can be useful in reducing the laboratory test protocol needed for the determina-tion of the optimal mix composition.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Tailings; Cemented backfill; Optimization; Mine; Response surface method; Desirability; Strength

1. Introduction

Cemented tailings backfill (cemented paste backfill stud-ied in this paper) is a heterogeneous material in which tail-ings are held in place by a hardened cement paste binder.Its components (tailings, water, cement) are combinedand mixed in a plant usually located on the surface andtransported (by gravity and/or pumping) to the under-ground mine (Fig. 1). Cemented tailings backfill (CTB) isextensively used in Canadian underground mines and inmany parts of the world and is following an increasingtrend as it offers a number of technical and economical

benefits (Lerche and Renetzeder, 1984; Landriault et al.,1997; Hassani and Archibald, 1998; Fall and Benzaazoua,2003a). Indeed, the CTB technology is considered superiorto conventional mine backfill methods in terms of cost-effectiveness (Hassani and Archibald, 1998; Fall and Ben-zaazoua, 2003b). It is especially important in ensuring thestability of underground mine openings and in maximizingthe safe recovery of ore. In addition, the maximum under-ground disposal of mill tailings is a significant environmen-tal advantage (Huynh et al., 2006).

In order for the CTB to assume the aforementionedroles in a safe and cost-effective manner in undergroundmining, proper proportioning of the CTB mixtures is nec-essary. In other words, the mix proportioning of CTB isa vital step in obtaining a CTB that meets desired technical

0886-7798/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.tust.2006.08.005

* Corresponding author. Tel.: +1 613 562 5800x6558.E-mail address: mfall@eng.uottawa.ca (M. Fall).

www.elsevier.com/locate/tust

Available online at www.sciencedirect.com

Tunnelling and Underground Space Technology 23 (2008) 80–90

Tunnelling and

Underground Space

Technologyincorporating Trenchless

Technology Research

and economical design requirements. The technical designrequirements in question are sufficient compressionstrength (generally between 0.7 and 2 MPa according toBrakebusch, 1994), acceptable technical consistency (fre-quently measured by slump test) and high solid concentra-tion (70–85%). While the economical design requirement isthat the cost of the CTB must be low. This cost depends onthe binder consumption. The binder can represent up to75% of the cost of the CTB (Grice, 1998).

However, there are no guideline or specifications on CTBmix proportions. In fact, CTB mix proportioning today isstill based primarily on traditional experimental methods.The latter require a large number of trial mixes to determinethe desired concentrations of the CTB components, whereasa good mix proportioning method serves to minimize thenumber of trial mixes and provides a satisfactory, economi-cal mixture possessing the desired properties (Bharatkumaret al., 2000). This lack of engineering approach for mix pro-portioning of CTB is due to several factors. On the one hand,CTB is a relatively new, complex cemented material which isdifferent from concrete (Fall et al., 2005a); studies on CTBhave only been ongoing for about 15 years. At the same time,the majority of the studies performed on the optimising ofCTB properties (Archibald et al., 1995; Amaratunga andYaschyshyn, 1997; Hassani and Archibald, 1998; Kesimalet al., 2003; Fall et al., 2004) were only experimental and

did not simultaneously take into account all of the perfor-mance properties of the CTB. These works were based pri-marily on the experience of the experts and for the mostpart, have only allowed a qualitative evaluation of the qual-ity of CTB mixes. Unfortunately, these studies are often lar-gely affected by subjectivity. Additionally, the mathematicalapproach for the analysis and modeling of performanceproperties of CTB has not been considered until now in thistype of study.

Considering the aforementioned problems and the factthat today’s increasingly competitive environment in themining industry, combined with strict environmental(Benardos et al., 2001) and safety legislations, demand ahigher quality CTB production in a shorter time, the goalof the research was:

� to develop a methodological approach and mathemati-cal models for CTB mix proportioning in order to min-imize the number of trial mixes and provide appropriatemix proportion;

� to predict the technical (compression strength, slump,%Solid) and economical (binder cost) performanceproperties of the CTBs studied;

� to analyze the interactions between the main compo-nents of CTB and their effect on its properties;

� to develop optimal mixes for the CTBs studied.

2. Methodology

Fig. 2 shows the methodological approach that wasdeveloped and the different steps for predicting the perfor-mance properties of CTB and for optimizing its mixture.The methodology comprises three main stages: experimen-tal, modeling, and optimization stage.

The purpose of the first experimental study was to iden-tify and assess the effects of the physical and chemical prop-erties of the main components of CTB (tailings, water,binder) on its mechanical (compression strength) and phys-ical (slump, %Solid) properties. The main results of thisexperimental investigation are given in Benzaazoua et al.,2004; Fall et al., 2004, 2005a, submitted. An analysis ofthe results made it possible to define the main mix param-

Response Surface

Methods based

Modeling

X1

X2

Xm-1

Xm

yi (UCS)

yk(costs)

yj(slump; %S)

Inputs

Tailings Binders Waters

Output 1 Output 2

Expert Tool

Analysis

Mai

n p

aram

eter

s

infl

uen

cing

CP

B

ster

ngth

OptimizationOptimal Mixes

Experimentalstudy

Fig. 2. Developed methodological approach for mix proportioning of cemented tailings backfill (cemented paste backfill).

Fig. 1. Schematic presentation of the different phases of the technology of

cemented paste backfill (CTB): preparation, transport and underground

placing of the CTB, where it builds CTB structure.

M. Fall et al. / Tunnelling and Underground Space Technology 23 (2008) 80–90 81

eters influencing the performance properties of CTB (com-pression strength, slump, %Solid, cost) and also to deter-mine the limits of the experimental domains of themodels to be developed. It has been experimentally demon-strated that, for a given curing time and conditions (e.g.temperature, humidity), the performance properties ofCTB are most influenced by the following characteristicsof its components (tailings, water, cement):

� the physical (grain size, density), chemical (sulphur con-tent, etc.), and mineralogical properties of the tailingmaterials;

� the type and quantity of the binders used;� the quantity and chemistry (sulphate content) of thetotal mixing water (added water and remaining tailingpore water) of the CTB.

In the second stage, these identified parameters were usedas basis data for the modeling. The latter made it possible topredict the uniaxial compressive strength (UCS), slump,solid concentration (%Solid), and cost (based on binder cost)of the studiedCTBs.Themodeling is basedon the techniquesof the response surface method. All fundamental aspects oftheRSMare given inBoxandWilson (1951),Khuri andCor-nell (1987), and Myers and Montomery (1995).

Since the CTB produced by the backfill plant must sat-isfy the following criteria: safety (sufficient mechanicalcompression strength), transportability (adequate slumpor solid concentration), physical–environmental properties(satisfactory solid concentration), and economics (low bin-der cost, profitability), optimization of the CTB productionconstitutes a necessary third stage. In this stage, the mod-eling results were used as input data. The optimization con-sisted of maximizing a function of desirability (Harrington,1965; Derringer and Suich, 1980) which takes into account,simultaneously, all the criteria important to the miningcompany (work safety, feasibility, and profitability of theCTB technique). The analysis and programming ofthe equations developed during the modeling stage led tothe development of a computer tool for the mix propor-tioning of the studied CTBs.

In this paper, methods and models for mix proportion-ing of CTB not confronted with a sulphate attack will bepresented (i.e. CTB with low sulphate content<500 ppm). The methods and models for binder mixturesoptimization of CTB affected by sulphate attack are pub-lished in Fall and Benzaazoua (2005). This paper will alsofocus on the results of the modeling and optimizationstudy. The results of the experimental study are describedelsewhere (e.g. Benzaazoua et al., 2004; Fall et al., 2004).

3. Material and testing methods

3.1. Materials

The materials used include binders, tailings and water.

Binders. Portland cement type I (PC I) and blast furnaceslag (Slag) were used as binders. PC I was blended withblast furnace slag (Slag) in a ratio of 20/80.

Tailings. Tailings (tailing A and tailing B) sampled fromtwo polymetalic mines (Mine A and Mine B) in easternCanada were used. The tailings materials of Mine A andB are characterized by a relative high amount of sulphideminerals (pyrite; 20–30% in weight). However, the tailingscontain only small amount of contaminants such as Pb(<0.1%), As (<0.02%), Cu (<0.02%). The sampled tailingswere reprocessed to create tailings with different particlesize distribution and densities. The relative mass propor-tions of fines F (particle size <20 lm) present in the tailingwere used to identify differences among the tailings used.Rinsing of the tailing materials (A and B) with tap waterallowed for the elimination or drastic reduction of the sul-phate present in the prepared tailing materials.

Water. Tap water was used to mix the binders and thetailings.

3.2. Preparation of test specimens

To produce CTB mixtures, the tailing materials, cementand water were mixed and homogenized in a double spiralmixer. Next, slump tests were performed to evaluate theCTB transportability. The CTB mixtures produced werethen poured into curing moulds, 10 cm in diameter and20 cm high. The poured specimens were sealed and curedin a humidity chamber maintained at approximately 80%humidity (similar to humidity conditions in Canadianunderground mines) and at a temperature of approxi-mately 23 �C for a period of 28 days.

3.3. Testing of specimens

To evaluate the technical and economical properties ofthe CTB specimens produced, the following propertiesand their relative importance were determined for eachspecimen:

� compressive strength up to 28 days after curing at23 ± 2 �C according to the ASTM C 39 standard usinga computer-controlled mechanical press (MTS 10/GL);

� slump of the fresh CTB mixtures. The latter was mea-sured by a slump test according to ASTM C 143-90;

� solid concentration or solid percent. The latter is theratio of the mix solids weight (tailings and binder) tothe weight of the total mix (water and solids);

� cost of each specimen. Based on evaluation of the cost ofthe quantity of binder used. The latter was calculatedfrom the mix proportions using the cost for each binderreagent (eastern Canadian market price in 2002).

In addition, SEM observations and Mercury IntrusionPorosimetry (MIP) measurements were performed on someCTB samples to characterize their microstructure.

82 M. Fall et al. / Tunnelling and Underground Space Technology 23 (2008) 80–90

4. Modeling the properties of cemented paste backfill

4.1. Modeling approach

Based on the results obtained in the preliminary experi-mental phase (Benzaazoua et al., 2004; Fall et al., 2004,submitted), the following four factors were chosen todescribe the ‘‘cemented paste backfill’’ system:

� X1 = %Cement; represents the type and quantity ofcement used;

� X2 = W/C; weight ratio of the quantities of water andcement used;

� X3 = %Fine; mass proportion of fine particles (<20 lm)in the tailings;

� X4 = qt (g/cm3); density of the tailings used.

The sulphate concentration of the combined mixingwaters (tailing pore water and added water) was main-tained constant (<500 ppm). The measured responses were28-days UCS (uniaxial compressive strength of the CTBafter 28 days curing time), slump, %Solid and the cost ofthe CTB. Fig. 3 shows a schematic representation of thedeveloped models.

The effects of these factors on CTB performance proper-ties were studied by experimental design. An orthogonalcentral composite design (CCD) (Khuri and Cornell,1987; Myers and Montomery, 1995) was used for develop-ing the material models for the CTB. The experiments wererun randomly and five levels of variables were used in theexperimental design. Based on the results of the experimen-

tal stage (Benzaazoua et al., 2004; Fall et al., submitted)and the cost of binders, the ranges of these four factorswere determined as shown in Table 1. It should be notedthar a binder proportion higher than 7% is not economi-cally feasible in the Canadian mining industry. To simplifythe calculation and avoid numerical error in the computercalculation, the variables X1, X2, X3,X4 are transformed todimensionless variables x1, x2, x3, x4 (coded values) accord-ing to Eq. (1).

Eq. (1) is shown below:

xi ¼X i � X 0

i

DX i

ð1Þ

where xi is the coded value, Xi is the corresponding actualvalue, X 0

i is the actual value at the center point, and DXi isthe step change value.

4.2. Results and discussions

4.2.1. Model development and analysis

The second-order polynomial, given by Eq. (2), wasused to fit the data of the experimental design.

Eq. (2) is shown below

y ¼ b0 þX

k

i¼1

bixi þX

k

i¼1

biix2i þ

XX

k

i<j

biixixj þ e ð2Þ

where y is the predicted responses (i.e. compressionstrength, slump, %Solid, cost of the studied CTBs), b0 isthe intercept term, bi, bii, bij are the constant regressioncoefficients for the linear terms, the pure quadratic terms,and the cross-product terms respectively. The xi variablesrepresent the normalized values of each of the input param-eters that influence the response y, the cross-term xixj rep-resents the first-order interactions between xi and xj, andthe square terms x2i represent second-order non-linearity.Finally, e is the associated random error reflecting the com-bined effects of variables not included in the models. It isassumed that the additive error e is normally distributedwith a mean of zero and standard deviation r.

Standard analysis of variance (ANOVA) and linearregression techniques were used to estimate the model’sparameters. The available commercial software JPM wasused. The performed statistical analysis made it possibleto develop four response surface models for predictingthe UCS, slump, %Solid, and cost of the studied CTBs.Because the UCS, slump and cost of the CTB vary over

x1

x2

x4

RSM based

modeling

Inputs

Cost

UCSx3

Slump; %S

Outputs

Fig. 3. Schematic presentation of the developed models: cost in $/t (Can

$/ton solid); slump in cm; %S, solid percent; UCS in kPa.

Table 1

Experimental range definition

Variables (Xi) Codes xi �2 �1 0 1 2

%Cement X1 0.8 2.8 4.8 6.8 8.8

W/C X2 6.2 7.0 7.8 8.5 9.3

%Fine (F) X3 10 30 50 70 90

qt tailings density (g/cm3)a X4 – 3.3 3.4 3.5 –

a (–): The two axial coded values of variables tailings density were different from �2 to 2 due to the technical difficulty to obtain tailings having the

corresponding densities and grain size distribution.

M. Fall et al. / Tunnelling and Underground Space Technology 23 (2008) 80–90 83

several orders of magnitude for the conditions consideredin this study, the log of UCS, slump and cost were used.

The main results of the regression analysis are summa-rized in Tables 2 and 3. Table 2 shows the main resultsof the analysis of variance and lack-of-fit, while the coeffi-cients of the determination of the models are given in Table3. The results of the regression analysis clearly highlightthat quadratic function material models can give reliablepredictions for the compression strength, slump, solid per-cent and cost of CTB. The models show high F-value(Table 2). The coefficients of determination (Table 3) forall models are very high (>0.97). It means that more than97% of the variations of the lnUCS, lnSlump, lnCost,and %Solid are caused by the variations in the input vari-ables x1, x2, x3, x4 (%Cement, W/C, %Fine, and qt).

The results of the variance analysis have also demon-strated that:

� the factors that significantly influence the compressionstrength (28-days UCS) of the CTB are: %Cement, theW/C ratio, the tailings grain size (%Fine) and the tail-ings density. The interactions between cement and W/C and between W/C and density also play a significantrole in the CTB hardening process (P < 0.01). The qua-dratic terms x21, x

23 and x24 are also statistically significant

(P < 0.01). The non-negligible effect of the interactionsbetween the model parameters demonstrates the non-additive character of the relation describing the 28-daycompression strength development of CTB;

� the %Cement, %Fine and density factors significantlyaffect the slump of the CTB (P < 0.0001). The interac-tions between the cement or density and the tailingsgrain size are statistically significant (P < 0.02). The per-cent fine (%Fine) and qt interact very synergistically forhigher slump. The square terms x21 and x23 also play a nonnegligible role (P < 0.03);

� the cost of the CTB, as expected, essentially depends onthe quantity of cement used and the tailings grain sizeand density (P < 0.001). The interaction between cement(x1) and tailings density (x4) is highly significant atP < 0.05. There is an antagonistic effect between thecement and density. This means that increasing the tail-ings density has a negative effect on the cost of CTB andleads to higher binder consumption;

� the solid percent is essentially controlled by the%Cement, W/C, %Fine and qt variables. The squareterm x21 is also statistically significant.

The results of the lack-of-fit analysis, summarized inTable 2, show that there is an insignificant lack-of-fit. Thus,the developed models (lnUCS28-days, lnSlump, %Solid,lnCost) are adequate in representing the true relationshipsin the current experimental region. The predictive modelsdeveloped were then applied to simulate the effects of themodel parameters (%Cement, W/C, tailings grain sizeand density) on the performance properties of the studiedCTBs.

4.2.2. Effect of model parameters on CTB compression

strength

Fig. 4 illustrates the effects of binder proportion, W/C,and tailings grain size and density on 28-days UCS. Asexpected, increasing the amount of cement leads to higherCTB compression strength. The reason for this increase isthat higher cement content leads to the formation of morecement hydration products, which in turn leads to a highercompression strength of the cement matrix (Mehta, 1986).It may also be noted that the lower the W/C ratio for anygiven binder proportion or tailing grain size, the higher theCTB compression strength becomes (Fig. 5). The increaseof CTB compression strength with decreasing W/C ratiois mainly caused by the subsequent decrease in overallporosity due to the once water-filled voids (Amaratungaand Yaschyshyn, 1997).

From Fig. 4, it can be also observed, that fine tailingsgrain size (20 lm particles >60 wt%) is not conducive tocompression strength development. Medium (35–60 wt%of 20 lm particles) and coarse (15–35 wt% of 20 lm parti-cles) tailings grain size are more conducive to CTB com-pression strength development. The highest compressionstrength is reached when the tailings contain 40–45% fineparticles (<20 lm). Fig. 4 suggests that a proportion of40–45% fines by mass seems to be the optimal tailings grain

Table 2

Main results of the analyses of variance and lack-of-fit

Models Analyse of variance Analyse of lack-of-fit

F Prob > P F Prob > P

lnUCS28-days 65.0 <0.0001 1.7 0.2

lnSlump 85.5 <0.0001 2.9 0.1

%Solid 96.2 <0.0001 1.6 0.2

lnCost 32188.7 <0.0001 0.2 0.9

Table 3

Coefficient of determination of the different models

Models lnUCS28-days lnSlump %Solid lnCost

R2 0.97 0.97 0.99 0.99

R 0.95 0.96 0.99 0.99

R2, coefficient of determination; R, adjusted coefficient of determination.

2.8 6.8 7.0 9.3 30 70 3.38 3.504.8 8.7 55 3.45

ρt (g/cm³)%FineW/C%Cement

1096

UC

S28-d

ays

2000

445

Fig. 4. Prediction profile of UCS 28 days (UCS in kPa).

84 M. Fall et al. / Tunnelling and Underground Space Technology 23 (2008) 80–90

size to obtain the highest compression strength for theCTBs studied (when the binder used is Portland cementtype I and slag blended in the 20/80 ratio). However, itcan be seen that at certain levels of tailings coarseness(25–35% of fine particles), the CTB compression strengthdecreases slightly. The observed increase of CTB compres-sion strength with tailings coarseness can be explained bythe fact that an increase in the tailings coarseness reducesthe overall porosity of the CTB and also leads to the refine-ment of the hardened cement matrix pores. This is due tothe reduction of both the W/C ratio of the CTB and thepacking density of tailing materials associated with increas-ing tailings coarseness (Fall et al., 2004). This decrease inporosity leads to compression strength gain. Another rea-son for the increase in CTB compression strength with tail-ings coarseness is the influence of the tailings particle sizeon the specific surface of the tailing material as reportedin Fall et al. (2004). However, it can be also seen inFig. 4 that a certain levels of tailings coarseness (25–35%fine particles), CTB strength decreases slightly. Thisdecrease can be attributed mainly to the negative effect ofthe increase of the capillary porosity of the interfacial tran-sition zone (ITZ) between the large tailings particles andthe cement matrix associated with increasing tailingscoarseness. It is well known (e.g. Monteiro et al., 1985;Garboczi and Bentz, 1991) that the higher the porosity ofthe ITZ, the weaker the bond between aggregates particles.The ITZ as a weakness zone inside CTB is qualitativelydemonstrated by the Fig. 6. This figure shows a SEMimage of CTB subjected to a uniaxial compression test. Itcan be clearly observed that the microcracks (induced bythe compression stress) propagate in the ITZ around thecoarser tailings particles. Additionally, Fig. 7 demonstratesthat for a given CTB mix, increasing of tailings coarsenessis associated with increasing proportions of macroporosity(0.1–1 lm). From Fig. 7, it can be seen that at 25% finescontent, the proportion of macropores (1–10 lm) withinthe CTB increases drastically. This higher proportion ofmacropores (1–10 lm) due to the ITZ may be the causeof the small decrease in the compression strength of cemen-ted paste backfill made from coarse tailings (25% fines) as

compared to CTB specimens made from tailings containing40–50% fine particles.

Fig. 4 demonstrates also that the tailings density affectsthe CTB compression strength development. After a den-sity value of 3.40 g/cm3, the UCS increases with the tailingsdensity. This increase is due to higher binder consumptionin volume (Fall et al., 2005a). However, the higher the tail-ings density, the higher the CTB production cost (Fig. 12).

These modelling results of the effects of the modelparameters on the compression strength of CTB corre-spond well with the results of the experimental tests carriedout on CTB by several authors (e.g. Hassani and Archi-bald, 1988; Archibald et al., 1995; Benzaazoua et al.,2003; Kesimal et al., 2004; Fall et al., 2004, submitted).

4.2.3. Effect of model parameters on CTB slump

The effects of the binder proportion and tailings grainsize and density on the CTB slump is presented in Fig. 8.As expected, higher binder proportions confer higher

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

3.0 3.5 4.0 4.5 5.0

Cement content (%)

UC

S (

kP

a)

W/C = 6

W/C = 7

W/C = 8

W/C = 9

Fig. 5. Effect of W/C ratio on UCS 28 days of the CTB for different

binder contents (%Fine = 40%; tailings density, qt = 3.459 g/cm3).

Fig. 6. SEM image shows that microcracks propagate around the tailings

particle at the ITZ (interfacial microcracks), which represents a weakness

region in CTB: T, tailings grain; CM, cement matrix; TZ, interfacial

transition zone (ITZ).

0

5

10

15

20

25

30

Hg

in

tru

sio

n p

oro

sity (

%)

75 55 40 25

% Fine

> 0.05 µm

0.05 - 1 µm

1 - 10 µm

> 10 µm

Pore size range

Fig. 7. Effect of tailings fineness on pore size distribution of paste backfill

specimens cemented with PCI/Slag after 28 days of curing (4.5% Cement

used).

M. Fall et al. / Tunnelling and Underground Space Technology 23 (2008) 80–90 85

CTB slump, since they increase the average distancebetween the tailings particles, thus reducing the inter-tail-ings particle friction, collision and subsequent blocking.However, the slump decreases as the tailings densityincreases. Tailings fineness also has an effect on the CTBslump (Fig. 9). Indeed, CTB made from finer tailings exhib-its lower slump. The most common reason for this decreaseof CTB slump with tailings fineness for a given W/C ratio isthat the fine tailings particles increase the water demand ofthe CTB due to the increase in surface area and availablevoid spaces between tailings particles (Ferraris and DeLarrard, 1998).

4.2.4. Effect of model parameters on CTB solid percent

In Fig. 10, the variation of the solid percent related tothe cement content, W/C, %Fine and tailings density isplotted. As anticipated, it can be observed that the solidconcentration is very sensitive to cement content andW/C ratio variations as illustrated in Fig. 11.

4.2.5. Effect of model parameters on CTB cost

The effects of cement content, W/C and tailings grainsize and density on the cement cost of the CTB are clearlyshown in Fig. 12. As expected, the cost of the CTB ismainly controlled by the cement content. However, the tail-ings grain size and density have a non-negligible influenceon the cost (Fig. 13). This can be attributed to the fact thathigher proportions of fine tailings particles reduce the

packing density (more void spaces available) of the tailingsparticles and thus increase the voids that must be filled by thecement paste. This results in higher cement consumption.

2.8 6.8 7.0 9.3 30 70 3.38 3.54.8 8.7 55 3.45

ρt (g/cm³)%FineW/C% Cement

%S

olid

88

58

73

Fig. 10. Prediction profile of the solid percent of the CTB.

55

60

65

70758085

2.8 6.84.8

6.2

9.3

7.8

8.5

7.0

% CementW

/C3.8 5.8

Fig. 11. Contour plot for solid percent versus % Cement and W/C.

2.8 6.8 7.0 9.3 30 70 3.38 3.504.8 8.7 55 3.45

(g/cm³)%FineE/C% Cement

6.0

1.8

10.0

Co

st

ρt

Fig. 12. Prediction profile of Cost (Cost in Can $/t solid).

% Cement

%F

ine

2.8 6.84.83.8 5.8

30

80

50

70

40

60

20

7.4

4.5

2.7

1.7

Fig. 13. Contour plot for CTB cost (in Can $/t) versus %Cement and

tailings fineness.

2.8 6.8 3.38 3.504.8 3.45

%Fine% Cement

30 7055

(g/cm³)

Slu

mp 22

30

9

ρt

Fig. 8. Prediction profile of slump (slump in cm).

0

5

10

15

20

25

30

35

40

35 40 45 50 55 60 65 70

%Fine grain size (<20 µm)

Slu

mp (

cm

)

3% Cement

4% Cement

5% Cement

Fig. 9. Effect of tailings grain size on the slump of CTB for different

binder contents (W/C = 7; tailings density, qt = 3.459 g/cm3).

86 M. Fall et al. / Tunnelling and Underground Space Technology 23 (2008) 80–90

Finer tailings also have a higher specific surface; conse-quently, more cement paste is needed to cover them thancoarse tailings. As the tailings density increases, the costof CTB likewise due to a higher binder consumption (involume) associated with increased tailings density. Theseobservations are in perfect agreement with the results ofthe experimental investigations carried out by Fall et al.(2004, 2005a).

4.2.6. Model validation

To verify the validity of the developed models, theresults of the model predictions were compared with exper-imental data from other studies (e.g. Benzaazoua et al.,2003, 2004; Fall et al., 2004, 2005a) and those obtainedfrom conducting additional experimental tests. The resultsof the experimental verification of the accuracy of the mod-els, presented in Figs. 14–16 and Table 4, show that there isa good agreement between model predictions and experi-mental observations.

5. Optimization

5.1. Approach

The aim of the optimization is to find optimal CTBmixes that allow the production of cost-effective (high qual-ity) cemented paste backfill. This means that the CTB pro-duced in the plant must simultaneously satisfy severalcriteria. These are:

� sufficient compression strength; i.e. the strength of theCTB produced must be higher than the critical designstrength. This will ensure the stability of the under-ground CTB structures;

� acceptable slump; this will allow the transportability ofthe fresh CTB;

� highest (possible) solid concentration; the solid concen-tration of the CTB should be maximized in order toreturn the maximum quantity of mine wastes to theunderground;

� lowest cost; the cost of the CTB must be as low as pos-sible; i.e. the binder consumption must be minimized.

Multi-criteria decision-making according to Derringerand Suich (1980) was applied to develop optimal CTB mix-tures. Fig. 17 illustrates schematically the optimization

500

800

1100

1400

1700

2000

2300

500 800 1100 1400 1700 2000 2300

UCS in kPa (experimental)

UC

S in k

Pa (

pre

dic

ted)

Fig. 14. Comparison of predicted UCS with those based on experimental

tests.

60

65

70

75

80

85

90

60 65 70 75 80 85 90

Solid percent (calculated)

Solid

perc

ent (p

redic

ted)

Fig. 15. Comparison of predicted solid percent with those evaluated

(based on laboratory solid percent evaluation).

1.90

2.90

3.90

4.90

5.90

6.90

7.90

8.90

9.90

10.90

11.90

1.90 3.90 5.90 7.90 9.90 11.90

Cost in $/t (calculated)

Co

st

in $

/t (

pre

dic

ted

)

Fig. 16. Comparison of predicted CTB costs with those calculated (based

on laboratory price evaluation).

Table 4

Selected results from verification trials for slump

%Cement W/C %Fine qt (g/cm3) Experimental

values

Predicted

values

4.5 9.1 68 3.4080 17.5 18.0

4.5 8.4 61 3.4271 17.5 20.7

4.5 6.4 33 3.4981 17.5 18.5

6.8 8.5 35 3.4981 29.5 27.3

2.8 10 35 3.4981 15.0 14.3

2.8 8.5 65 3.4271 10.0 10.5

4.8 10.6 50 3.4481 29.0 28.3

4.8 9.2 50 3.4481 29.0 27.0

M. Fall et al. / Tunnelling and Underground Space Technology 23 (2008) 80–90 87

approach. The developed predictive models (lnUCS,lnSlump, %Solid, lnCost) are used as input data. First,the desired CTB properties (desired compression strength,slump, %Solid, cost), i.e. quality characteristics that theCTB must fulfil, were defined. Each desired CTB propertyhas a target value and/or specification limits (upper, lowerlimit). After determining the desired CTB properties, amulti-criteria optimization (Derringer and Suich, 1980)was performed to find solutions to this problem, i.e. to findthe CTB mixes that meet the desired quality characteristics.This multi-criteria optimization is based on the construc-tion of a desirability function (Harrington, 1965; Derringerand Suich, 1980) for each individual model response Yi

(lnUCS, lnSlump, %Solid, lnCost). Hence, a desirabilityfunction (di) was first determined for each response Yi.Based on these individual desirability functions, the overalldesirability function was estimated as the weighted geomet-ric mean of the individual desirability functions, whichgives the overall desirability D. The overall desirabilityfunction is defined by

D ¼Y

q

i¼1

drii

! 1P

ri

ð3Þ

where di is individual desirability and ri is a value between 1and 5. The choice of the value of ri is made based on thesubjective importance of this objective in the CTB design.

5.2. Results and discussions

By applying the optimization approach described in theprevious section, optimal recipes were developed for theCTBs studied. The optimized responses and their desiredranges are given in Table 5. Assuming equal importance(r1 = r2 = r3 = r4 = r5) for the four CTB properties(Y1 = lnUCS, Y2 = lnSlump, Y3 = lnCost, Y4 = %Solid),overall desirability has been calculated and desirabilityplots were constructed as a function of the componentsof the studied CTBs (%Cement, W/C, %Fine, qt) usingEq. (3). The main results of the optimization are summa-rized in Figs. 18–21.

SlumpD

CostD

Multicriteria-

optimization

Inputs(desired properties)

%SolidD

Optimal mixes

Outputs(solutions)

UCSD

Fig. 17. Schematic presentation of used approach to develop optimal

recipes for CTB: D, desired; CostD, desired cost (RSM based models

used).

Table 5

Optimized responses and their desired ranges

Responses Desired range

UCS 28 days (kPa) 700 < Y1 < 1000

Slump (cm) 15 < Y2 < 25; Y2 = 18; ideal slump

Cost ($/ta) 2 < Y3 < 6

%Solid 70 < Y4 < 85

a Can $/ton solid.

2.8 6.8 7.0 10 30 70

0.7

3.8

0

1

%FineW/C% Cement

Desirabitlit

y, D

47

Fig. 18. The overall desirability of the studied CTBs (tailings density

maintained constant at 3.46 g/cm3).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

2 3 4 5 6 7

%Cement

Desirabili

ty

%Fine = 45%

%Fine = 55%

%Fine = 65%

Fig. 19. Influence of the tailings fineness (%Fine) and cement proportion

on the overall desirability of the studied CTBs (W/C = 7; tailings density,

qt = 3.46 cm3/g).

0.4

0.5

0.6

0.7

0.8

6 7 8 9W/C

De

sira

bili

ty,

D

%Fine = 45%

%Fine = 55%

%Fine = 65%

Fig. 20. Influence of the tailings fineness (%Fine) and of W/C on the

overall desirability of the studied CTBs (%Cement = 3.8%; tailings

density, qt = 3.46 cm3/g).

88 M. Fall et al. / Tunnelling and Underground Space Technology 23 (2008) 80–90

Fig. 18 shows the overall desirability function (D) plot-ted against the cement content, the W/C ratio and the tail-ings grain size. The tailings density is maintained constantat 3.46 g/cm3. It may be noted that some desirability valuesare relatively high and that some approach zero. In Fig. 18,it is clear, for a given tailings density, that the quality of theCTB is mostly controlled by the cement content, the tail-ings grain size and the W/C ratio. This figure shows thatit is possible to reach a desirability of 0.7 with a cementcontent of 3.8% and a W/C of 7, using tailings materialswith a proportion of fine of about 47%.

Fig. 19 puts into perspective the influence of cementcontent on the overall desirability of CTB for different tail-ings fineness. It can be observed that the global desirabilityis very sensitive to small changes in cement content. Acement content lower than 3% or higher than 4.5% drasti-cally decreases the global desirability of CTB. A desirabil-ity higher than 0.4 can be reached for cement contentsranging between 3.3 and 4. It can also be seen that the tail-ings fineness plays an important role in obtaining highquality CTB. Fine tailings particle sizes confer the CTBlower desirability values.

Fig. 20 shows the influence of W/C ratio on the globaldesirability of CTB related to the tailings grain size. Adesirability value higher than 0.6 can be reached for a widerange of W/C ratios. W/C ratios ranging between 6 and 8.5are most conducive to attaining a high CTB desirability.

Fig. 21 shows a graphical presentation of the variabilityof the overall desirability function in regards to the%Cement and W/C factors. The %Fine and density factors

are maintained constant at 45% and 3.46 g/cm3 respec-tively. This plot indicates that the highest values for totaldesirability in this case were achieved for a W/C between7 and 8.5 and cement contents between 3.4 and 4.3. How-ever, although the %Fines and density factors remain con-stant in this plot, it can be seen that in the region aroundthe optimum, the optimum is more sensitive to changesin %Cement than to changes in W/C.

6. Summary and conclusion

In this study, a comprehensive engineering approach todesigning cost-effective CTB based on performance specifi-cations is proposed. This work has demonstrated the abil-ity of using the RSM and desirability approaches,respectively, as reliable tools for predicting and optimizingthe performance properties (UCS, slump, solid concentra-tion, and cost) of CTB. The methodological approachand the predictive models developed in this study providean appropriate and adequate consideration of the multiplefactors affecting the CTB properties and the prediction ofthe latter with relatively good accuracy. The modelingresults are in perfect agreement with those of experimentaltests undertaken by several authors (e.g. Hassani andArchibald, 1988; Archibald et al., 1995; Amaratunga andYaschyshyn, 1997; Benzaazoua et al., 2003; Kesimalet al., 2003, 2004; Fall et al., 2004, 2005a, submitted).The optimization that was performed, based on multi-crite-ria optimization techniques, has enabled the developmentof cost-effective mixes of the studied CTBs. Valuableresults were also gained regarding factors controllingCTB properties, the interactions between its main compo-nents (cement, tailings grain size and density, W/C ratio,cement ratio, mixing water) and their effect on its behav-iour, etc. It was demonstrated that the cement content,the tailings fineness, the W/C ratio, and the tailings densitysignificantly affect the performance properties of CTB.However, the expert tool developed in this study for thedesign of cost-effective underground cemented backfillshould not exclude the undertaking of the essential labora-tory experimental tests. The methodological approachdeveloped in this study can be applied to any CTB to pre-dict and optimize its properties. It will permit a thoroughassessment and a significant reduction in subjectivity whenevaluating the quality of CTB.

However, in spite of the interesting results obtained in thiswork, additional research is necessary in order to consider alarger experimental range definition, to take into accountchanges in the mineralogical or petrographical nature ofthe tailings material (since the latter can differ from one min-ing region to another), and to test other binder types.

Acknowledgement

This work was sponsored by IRSST (‘‘Institut deRecherche Robert-Sauve en sante et en Securite duTravail’’).

3.00 3.50 4.00 4.50 5.00 5.50

%Cement

6.00

6.50

7.00

7.50

8.00

8.50

9.00

W/C

Fig. 21. Contour plot of the overall desirability function in the space of

the factors %Cement and W/C (%Fine = 45%; tailings density,

qt = 3.46 cm3/g).

M. Fall et al. / Tunnelling and Underground Space Technology 23 (2008) 80–90 89

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