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56TH CANADIAN GEOTECHNICAL CONFERENCE 56ième CONFÉRENCE CANADIENNE DE GÉOTECHNIQUE 4TH JOINT IAH-CNC/CGS CONFERENCE 4ième CONFÉRENCE CONJOINTE AIH-CCN/SCG 2003 NAGS CONFERENCE 2003 NAGS CONFÉRENCE MODELING AND SIMULATION OF PASTE BACKFILL PERFORMANCE PROPERTIES 1 Mamadou Fall* , Ph.D., URSTM-University of Quebec in Abitibi-Témiscamingue, Canada Mostafa Benzaazoua, Ph.D., URSTM-University of Quebec in Abitibi-Témiscamingue, Canada ABSTRACT: A methodological approach and response surface models were developped is this study to predict the performance properties of paste backfill and optimize its mixture. The predicted properties are the uniaxial compressible strength (UCS), the slump, solid concentration (solid percent) and cost (based on cement cost) of the backfill. Using a central composite experimental design, the effect of tailings grain size and density, binders content, W/C ratio on these properties was determined. Statistical analysis revealed a highly significant (P<0.001) effect of all these variables. Following identification of the significant variables, response surface equations have been developped to predict the above performance properties of the backfill. The models were experimentaly validated. The programming of the developed equations led to the development of computer programm, which will help mining engineers to create cost effective paste backfill. The results of this study represent a significant advance in research on paste backfill technology and will greatly benefit the mining industry. RESUMÉ: Une méthode et des modèles mathématiques basés sur les techniques de surface réponse ont été développés dans cette étude pour prédire les propriétés des remblais miniers en pâte cimentés et optimiser leurs recettes de mélanges. Les propriétés sont: la résistance à la compression simple, la consistance (taux d’affaissement), la concentration en solide et le coût de la quantité de ciment utilisée. L’exécution d’un plan expérimental de type central composite a permis de mettre en évidence l’effet de la granulométrie du résidu, sa densité, de la teneur en liant, du rapport E/C sur lesdites propriétés. L’analyse statistique a mis en relief un effet très significatif (P <0.001) de toutes ces variables. Consécutive à cette analyse, des équations de surface réponse ont été développées. Celles-ci permettent la prédiction des propriétés des remblais. Les modèles développés ont été validés expérimentalement. La programmation des équations développées a permis de créer un outil d’aide à la confection de remblais économiques et effectifs. Les résultats de cette étude représentent une avancée significative dans la recherche sur les remblais en pâte et seront d’une grande utilité pour l'industrie minière. 1. INTRODUCTION bulk density, cost) of paste backfill. This paper presents the developed approach and mathematical model based Paste backfill is well established in many mines in the world on response surface method, which allows: and significant cost savings and operational benefits have - to predict the physical and mechanical performance of been realised, compared to other methods of fill. The the paste backfill in order to economize mining process application of paste fill could significantly reduce the and improve the safety in mining work; cyclical nature of mining, improve ground conditions, - to analysis the effect of the interactions between the speed up production and greatly reduce environmental components of backfill on its properties; costs related to tailings management on the surface - to estimate the cost of the produced paste backfill; (Hassani & Bois, 1992). However, paste backfill - to optimize the backfill mixture in order to reduce represents a relatively new technology in which several production cost of paste backfill. aspects (mechanical, chemical, physical, interactions between the components, etc.) are not yet completely understood. For example, many mining industries are 2. METHODOLOGY confronted with failures risk of paste backfill due to the difficulty to predict its performances properties and to Figure 1 shows the developed methodological approach develop rational and practical design approach upon and the different work steps for predicting the which operators can effectively manage backfill performance properties of paste backfill and for optimizing technology. its mixture. The methodology includes three main stages: experimental, modeling and optimization stage. Hence, multi-disciplinary research programs are carried out at URSTM-UQAT by the above authors to develop a First experimental study was undertaken to identify and methodological approach and mathematical models for assess the effect of the physical and chemical properties predicting the performance properties (strength, slump, of the main components (tailings, water, binder) of paste *Corresponding author : Dr. Mamadou Fall, URSTM (Unité de Recherche en Science et Technologie Minérale)- University of Quebec in Abitibi-Temiscamingue; 445, boul. de l'Université; Rouyn-Noranda (QC) J9X 5E4; Fax: (819) 797-4727; Email : Mamadou.Fall@uqat.ca backfill on its mechanical (strength) and physical (slump, Tailings Binders Waters Expert Tool bulk density) properties. The main results of this experimental investigation are given in Fall & Benzaazoua Labo* Analysis 2003-a and Benzaazoua et al. 2003. The analysis of the results of this experimental study has allowed to define Inputs Output 1 Output 2 the main parameters influencing the performance of paste X1 yi (UCS) Parameters which backfill strength influence paste backfill. It has been experimentally demonstrated that the X2 Response Surface Y(UCSoptimal) yj(slump) Methods based Optimization mechanical and physical properties of paste backfill are Mix opt. Xm-1 Modeling yk(costs) most influenced by following parameters: Xm - the physical (grain size, density) and mineralogical properties (sulphide content, etc.) of the tailing Figure 1. Developed approach for modeling the materials; performance properties of paste backfill and optimizing its - the type and the quantity of the used binders; mixtures *Labo: experimental stage - the curing time; - the quantity and chemistry (sulphate content) of the total mixing water (added water and remaining tailing 3. MATERIEL, SPECIMEN PREPARATION AND pore water) of the paste backfill. TESTING In the second stage, these identified parameters were 3.1 Material used used as basis data for the modeling. The latter allowed to predict the strength (uniaxial compressible strength), The used material included binder reagents, tailings and slump, cost of the used binder and bulk density of the water. paste backfill. The modeling is based on the techniques of response surface method (RSM). All fundamental aspects Binder reagents: Type I Portland cement (PC I) and blast of RSM are detailed described in the works of Box & furnace slag (Slag) were used. The two cement reagents Wilson (1951), Box & Drapper (1987), Khuri & Cornell were blended in the ratio 20/80. PC I and Slag, and this (1987) and Myers & Montgomery (1995). ratio are often used by the mining industry in eastern Canada for paste backfill mixtures. Since the paste backfill produced by the backfill plant must satisfy the criteria of safety (satisfactory mechanical Tailings: Tailings material from polymetalic mines located strength), technique, i.e transportability (slump ranging in eastern Canada were used as aggregates. The tailings between 15 cm and 25 cm) and economic (low binder contain about 16 % sulphide. The sulphide minerals are cost, profitability), an optimization of the paste backfill mainly represented by pyrite. The separation of the tailing production is necessary. Therefore, in a third stage, an materials by hydrocyclone has allowed to create several optimization of the paste backfill mixture was carried out. grain size classes from fine to coarse tailing. The particle- The modeling results were used as input data. This size distribution curve (figure 2) shows the range of optimization consisted to maximize a function of particle sizes present in the tailings samples and the type desirability (Harrington 1965, Derringer and Suich 1980) of distribution of these particles. This distribution covers a which takes into account, simultaneously, of the important wide range of possible particle size distribution of tailings criteria for the mining company (safety of the workers, from Canadian mines. The relative mass proportions of feasibility and profitability of the technique of paste fines F (particle size < 20 µm) present in the tailing were backfill). The analysis and programming of the equations used to identify differences among the used tailings. developed in the modeling led to the development of computer program which will help mining engineers to Water: tap water with low sulfate content, and mine create cost-effective paste backfill. process waters with high sulfate content were used. Globally, two main types of models were developed in this study. Models for predicting the performance of paste 100 backfill not confronted with sulphate attack (most frequent 90 % Fine case) and other models for backfill confronted with 70 Volume percent (cumulative) 80 sulphate attack. The first type of models will be presented 70 50 in this paper. The second type of models is presented 60 45 elsewhere (Fall & Benzaazoua, 2003-b). This paper will 23 50 be also focussed on the results of modeling and 80 40 optimization study. The results of the experimental study 25 30 are detailed described in the works of Benzaazoua et al. 30 2003, Fall & Benzaazoua 2003a. 20 10 10 0 0.01 0.1 1 10 100 1000 Grain size (µm) Figure 2. Grain size distribution of the used tailings 3.2 Preparation of test specimen - X1 = % cement; it represents the type and the quantity of used cement; The samples of tailing materials were received in barrels. - X2 = W/C; the weight ratio of the quantity of used water The tailings were then separated in different grain size and cement; classes by hydrocyclone. After that, the barrels were - X3 = % Fine (F); the mass proportion of fine particules homogenized. In order to produce paste backfill mixtures, (<20 µm) in the tailings; it well represents the grain the tailing materials, cement and water were mixed and size of the used tailings material. homogenized in a mixer with double spiral. The produced - X4 = ρt (g/cm³); the density of the tailings. paste backfill mixtures were poured into curing cylinders, 10 cm in diameter and 20 cm high. The poured The sulfate concentration of the total mixing waters specimens were sealed and cured in a humidity chamber (tailing pore water and added water) was maintained maintained at approximately 70% humidity (similar constant (<500 ppm). The measured responses humidity conditions in the underground mines) for periods (independent variables) were the uniaxiale compressible of 28 days. strength of the paste backfill after 28 days curing time (UCS 28-days), slump, %Solid and the cost of the 3.3 Testing of specimens quantity of used cement. Figure 3 shows a schematic representation of the developed models. The following properties were then determined on paste backfill specimens: - compressive strength up to 28 days after curing at 23 x1 ± 2°C according ASTM standards using a computer- controlled mechanical press (MTS 10/GL). The compressive strength testing allowed the determination of the uniaxial compressive strength (UCS) of the x2 tested samples, which corresponds to the maximum Cost stress observed during the test. The UCS is used in Backfill as Slump; %S the practice to judge the stability of the underground x3 black box UCSti backfill or backfill failure risk; - cost of each specimen. It is based on evaluation of the cost of the quantity of used binder. The latter was calculated from the mix proportions using costs for each binder reagent (binder cost applied at the eastern x4 Canadian market, Benzazoua et al. 2002). The binder can represent up to 75 % of the paste backfill Figure 3. Schematic presentation of the developed production cost (Grice, 1998); models - slump of the fresh paste backfill mixtures. The latter Cost in $/t (Can $/ tonne solid); Slump in cm; %S: solid was measured by slump test according to ASTM C percent; UCS in kPa. 143-90. The Determination of slump has allowed characterizing the paste backfill’s consistency that can The experiments were run in a random order. Five levels be related to its transportability; of variables were used in the experimental design. Based - solid concentration or solid percent (%). The latter is on the results of the experimental stage (Fall & the ratio of the solids (tailings and binder) in a mix to Benzaazoua, 2003) and on economical reasons (binders the weight of the total mix (water and solids). cost), the ranges of these four factors were determined as given in table 1. Indeed, a binder proportion higher than 7% is not economical feasible in the mining industry in 4. MODELLING Canada. To simplify the calculation and avoid numerical error in the computer calculation, the variables X1, X2, X3, The formulation and development of the mathematical X4 are transformed to dimensionless variables x1, x2, x3, x4 models (material models) is first based on the results of (coded values). The experimental design consisted of 16 the performed experimental design. These experiments factorial points, 8 axial or star points (two axial points on were undertaken, using a central composite design. The the axis of each design at a distance of ±2.0 coded units experimental results were then subjected to regression from the design center; 1 factor been level -2.0 or +2.0, analysis to obtain the parameters of the mathematical while others are maintained at zero level), and 6 central models for the dependent variables (UCS, Slump, Solid points for replications (to evaluate the experimental error). percent, Cost). The variables and their levels, both coded and actual units, selected for this study are shown in Table 1. The 4.1 Performed experimental design correspondence between the coded and actual values can be obtained using the equation (1) A rotatable orthogonal central composite design (Khuri and Cornell 1987, Myers and Montgomery1995) has been X - X0 used for developing the material models for the paste x= (1) backfill. The four following factors (independent variables) DX were chosen to describe the system “paste backfill”: where x is the coded value, X is the corresponding actual assess the adequacy of the models to represent the value, X0 is the actual value in the center of the domain, experimental data. and ∆X is the increment of X corresponding to 1 unit of x. Some results of the regression analysis are summarized Table 1. Experimental range definition in Tables 2 and 3. Table 2 shows the results of the analysis of variance, while the coefficients of the Codes xi -2 -1 0 1 2 determination of the models are given in table 3. The results of regression analysis clearly highlighted that Variables (Xi) % cement X1 0.8 2.8 4.8 6.8 8.8 quadratic function material models of paste backfill can W/C X2 6.2 7.0 7.8 8.5 9.3 give reliable predictions for the strength, the slump, the % Fine (F) X3 10 30 50 70 90 cost and solid percent. The models show high F-value ρt (g/cm³) X4 - 3.38 3.44 3.5 - (table 2). The coefficients of determination (table 3) are for all models very high (>0,97). It means that more that 4.2 Results and discussions 97% of the variations of the lnUCS, lnSlump, lnCost and solid percent are caused by the variations of the input 4.2.1 Model development and analysis variables x1, x2, x3, x4 (%cement, W/C, %Fine and ρt). Quadratic response surface models were constructed. Table 2. Results of the analyse of variance of the different nd models (table ANOVA) The below 2 order polynomial (equation 2) was used to develop predictive models for the strength (UCS28 days), the slump, the solid percent and the cost of the paste Source DF* Sum of Mean F Prob>P backfill. Because the UCS, slump and cost of the paste Models squares square backfill vary over several orders of magnitude for the Model 7 4.36 0.484 65.03 <0.0001 conditions considered in this study, the log of UCS, of lnUCS28 Error 20 0.14 0.007 slump and of cost were used. The polynomial has this days Total 27 4.50 form: Model 8 3.71 0.53 85.48 <0.0001 lnSlump Error 11 0.12 0.01 Total 19 3.83 4 4 Ym = b + å bi x i + å b ii x i2 + å å b ij x i x j + e (2) Model 14 2.95 0.21 11411 <0.0001 0 i=1 i=1 i j>i lnCost Error 26 0.00031 0.0018 Total 31 2.95 Model 5 1364.1 272.8 96.2 <0.0001 where, Ym (Y1 = lnUCS28days for the strength, Y2 = % Solid Error 26 73.7 2.8 lnSlump for the slump, Y3 = lnCost for the cost, Y4 = Total 31 1437.8 *DF: degree of freedom %Solid for the solid percent) are the predicted responses, b0 is the intercept, bi are constant regressions coefficients for the linear terms, bii are constant regressions Table 3. Coefficient of determination of the different coefficients for the pure quadratic terms; bij are constant models regressions coefficients for the cross-product terms. The xi variables represent the normalized values of each of Models lnUCS28 lnSlump lnCost % Solid days the input variables which affect the responses; the cross- r2 0.96 0.97 0.99 0.99 term xixj represent two-parameter interactions and square r 0.95 0.96 0.99 0.99 2 terms xi represents second order non-linearity. The 2 r : coefficient of determination; r: adjusted coefficient of determination 2 interaction-terms xixj and the quadratic terms xi account for curvature in the response surface. This curvature is The results of the analysis of variance have also frequently present when a response is at or close to demonstrated that: maximum or minimum. And finally, e is associated - the factors significantly influencing the strength (UCS random error; it represents the combined effects of 28 days) of the paste backfill are %cement, the W/C variables not included in the models. ratio, the tailings grain size (%fines) and the tailings density. The interactions between cement and W/C, The equation 2 was used to fit the data of the W/C and density, also play a significant role in the experimental design. All data were analyzed using backfill hardening process (P<0.01). The quadratic standard statistical software which estimates average 2 2 2 term x1 , x3 and x4 are also statistical significant effects, statistical significance, and regression coefficients (P<0.01). The non-negligible effect of the interactions for all variables and their interactions. T-tests were between the model parameters demonstrates the non- conducted to identify the most important b terms to additive character of the relation describing the 28-day include in the developed equations. Thus, square and strength development of paste backfill. interactions term which were below 95% confidence level - the factors %cement, %Fine and density significantly were discarded from the models through stepwise affect the slump of the paste backfill (P<0.0001). The regression. This has allowed the development of four interactions between the cement or density and the predictive models (lnUCS28 days, lnSlump, lnCost, tailings grain size are statistical significant (P<0.02). %Solid). Analysis of lack-of-fit was then performed to %Fine and ρt strongly interact synergetically for higher 2 2 slump. The square terms x1 and x3 also plays a non Figures 4, 6 and 7 show the influence of the tailings grain negligible role (P<0.03). size on paste backfill strength. Fine tailings grain size is - the cost of the paste backfill, as expected, essentially not favourable for the strength development. The highest depends on the quantity of used cement, the tailings strength is reached when the tailing contains 40 to 50 % grain size and density (P<0.001). The interaction fine particles (<20µm). Figure 7 suggests that a proportion between cement (x1) and tailings density (x4) is of 45 % fine by mass seems to be the optimal tailings strongly significant at P < 0.05. There is an antagonist grain size for the highest backfill strength (when the used effect between the cement and the tailings density. binder is Portland cement type I and slag; 20/80). This means, increasing the tailings density has a negative effect on the cost of paste backfill and leads 1400 to higher binder consumption. 1300 % Fine - the solid percent is essentially controlled by the 1200 30% 35% variables cement, W/C, % Fines, ρt. The square term 1100 40% 2 x1 is also statistical significant. UCS (kPa) 1000 45% 50% 900 65% The results of the analysis of lack-of-fit have shown that it 800 is not significant. Thus, the developed models are 700 adequate to represent the true relationships. 600 500 4.2.2 Simulations 400 2.5 3.0 3.5 4.0 4.5 Cement content (%) The developed predictive models were applied to simulate the effects of the model parameters (%cement, W/C, Figure 6. Evolution of UCS 28 days of the paste backfill tailings grain size and density) on the performance for different binder contents related to the grain size of the properties of the paste backfill. tailing (W/C = 7; ρt = 3.459) Figure 4 illustrates the effects of binder proportion, W/C, 1800 tailings grain size and density on lnUCS 28 days. As % Cement 2.5% expected, increasing the amount of cement leads to 1600 3.5% higher paste backfill strength. The higher the ratio W/C at 4.5% any given binder proportion or tailing grain size, the lower 1400 5.5% the strength at 28 days becomes (Figure 5). This decreasing of backfill strength with increasing of the W/C UCS (kPa) 1200 ratio is mainly caused by the subsequent increasing in overall porosity due to the once water-filled voids 1000 (Amaraunga & Yaschyshyn, 1997). 800 lnUCS28-days 7,61 7.61 600 6.96 6,964879 6.13 6,13 400 4.8 8.7 55 3.45 30 35 40 45 50 55 60 65 2.8 -0,0035 6.8 7.0 1,25931 9.3 30 0,16207 70 3.380,28887 3.50 % Fine grain size (<20 µm) %Cement % ciment W/C E/C %Fine F/G ρX(Gs) t (g/cm³) Figure 7. Effect of tailings grain size on UCS 28 days of Figure 4. Prediction profile of lnUCS 28 days (UCS in kPa) the paste backfill for different binder contents (W/C = 7; ρt = 3.459) 1700 W/C = 6 1500 Figure 4 and 8 demonstrate that the tailings density plays W/C = 7 W/C = 8 an important role in the backfill strength development. The 1300 W/C = 9 log of the UCS 28 days decreases with the increase of UCS (kPa) W/C = 10 tailings density as far as a density equal to 3.45 g/cm³ 1100 (figure 8). After this value, the log of UCS increases with 900 the tailings density. This increasing of UCS with the tailings density is due to higher binder consumption in 700 volume (Benzaazoua et al, 2003). However, the higher 500 tailings density, the more expensive is the cost production 3.0 3.5 4.0 4.5 5.0 of the paste backfill (Figures 9 and 10). Cement content (%) Figure 5. Effect of W/C ratio on UCS 28 days of the paste backfill for different binder contents (% Fine = 40%; ρt = 3.459) 2000 ρt = 3.400 2,5 257 3.4 1800 lnSlump ρt = 3.450 3.1 1600 2,2 30424 ρt = 3.500 1400 1,2 528 2.2 UCS (kPa) 1200 4.8 55 3.45 2.8 -0,0464 6.8 30 0,2 8571 70 3.38 0,2 7388 3.50 1000 % Cement % cime nt %Fine F/G ρX(Gs) t (g/cm³) 800 600 Figure 11. Prediction profile of lnslump (slumo in cm) 400 200 In Figure 12, the variation of the solid percent related to 2.5 3.0 3.5 Cement content (%) 4.0 4.5 5.0 the cement content, W/C, % Fine and tailings density is plotted. It can be observed that the solid concentration is very sensible to variations of the cement content and ratio Figure 8. Effect of tailings density on UCS 28 days of the W/C. paste backfill for different binder contents (W/C = 7; %Fine = 40%) 88 88 %Solid 1300 5 72.5 72,53998 73 1200 58,5 58 4.5 4.8 8.7 55/45 3.45 1100 2.8 -0,0565 6.8 7.0 1,3 071 9.3 30/70 5161 70/30 3.380,2 8832 3.5 0,1 1000 % Cement % cimen t W/C %Fine ρX(Gs) t (g/cm³) Cost (Can $/t) 4 E/C F/G UCS (kPa) 900 Figure 12: Prediction profile of the solid percent of the 800 3.5 paste backfill 700 3 4.2.3 Model validation UCS 28 days (kPa) 600 Cost (Can $/t) 500 2.5 In order to verify the validity of the developed models, the 3.40 3.42 3.44 3.46 results of the model predictions were compared with Tailings density (g/cm³) experimental data obtained by conducting additionally experimental tests (Fall and Benzaazoua, 2003a). The results of the experimental verification of the accuracy of Figure 9. Influence of the tailings density on the cost of the models are summarized in Table 4. It can be the used binder amount and on the UCS 28 days of the observed, there is a good agreement between model paste backfill (% cement = 3.8%; W/C = 7; %Fine = 40%). predictions and experimental observations. For example, the lnUCS model allows a good prediction of the backfill strength with an average predictions error of 8% falling 2,2 799 2.3 well within the relative standard uncertainty of 5 to 10% for the uniaxial compressible tests. lnCost 1.7612 1.8 1,7 61174 0,6 454 0.6 Tables 4. Selected results from verification trials 4.8 8.7 55 3.45 2.8 -0,0547 6.8 7.0 1,3 2875 9.3 30/70 4688 70/30 3.380,2 8807 3.50 0,1 Cem. W/C % Fi. ρt Expe Pred Err. % Cement % cimen t E/C E/C F/G F/G ρt (g/cm³) X(Gs) (%) value value (%) (g/cm³) Figure 10. Prediction profile of lnCost (Cost in Can $/t solid) 2.8 8.5 35/65 3.4981 1108 1033 6.7 6.8 8.5 35/65 3.4981 2000 1999 0.0 6.8 8.5 65/35 3.4271 910 1008 10.7 The effects of cement content, W/C, tailings grain size 2.8 10 65/35 3.4981 1207 1240 2.8 2.8 10 65/35 3.4271 486 446 8.2 and density on the cost (cement cost) of the paste backfill UCS 28 6.8 10 65/35 3.4271 602 627 4.2 are clearly shown in Figure 10. The cost of the backfill is days 4.8 9.3 50/50 3.4481 863 997 15.6 mainly controlled by the cement content. However the (kPa) 4.8 9.3 24/76 3.4981 1229 1184 3.6 tailings grain size and density has non-negligible influence 4.8 9.3 50/50 3.4481 1357 1210 10.8 on the cost (Figure 9). average error: 8% 4.5 9.1 68/32 3.4080 17.5 18.0 3.9 4.5 8.4 61/39 3.4271 17.5 20.7 19.2 The effect of the binder proportion, the tailings grain size 4.5 6.4 33/67 3.4981 17.5 18.5 5.9 and density on the slump of the paste backfill is presented 6.8 8.5 35/65 3.4981 29.5 27.3 8.3 Slump in Figure 11. As expected, higher binder proportions (cm) 2.8 10 35/65 3.4981 15.0 14.3 4.6 confer the paste backfill higher slumps. However, the 2.8 8.5 65/35 3.4271 10.0 10.5 4.3 slump decreases as the tailing density increases. The 4.8 10.6 50/50 3.4481 29.0 28.3 2.6 4,8 9,25 50/50 3,4481 29.0 27.0 7.2 fineness of the used tailing has also effect on the backfill average error: 9% slump. 2.8 8.5 35/65 3.4981 3.5125 3.49 0.6 In order to find the optimum backfill mixes, the principle of 6.8 8.5 35/65 3.4981 8.2134 8.25 0.5 multi-criteria optimization (Derringer and Suich, 1980) was 6.8 8.5 65/35 3.4271 8.2127 8.22 0.1 used. The latter is based on the desirability function first 2.8 10 65/35 3.4981 3.5136 3.49 0.6 developed by Harrington (1965). The desirability Cost 2.8 10 65/35 3.4271 3.5149 3.54 0.6 2.8 8.5 65/35 3.4271 3.5135 3.54 0.7 approach combines the multiple responses into a single ($/t) function and try to find the optimal mix. First, a desirability 6.8 10 65/35 3.4271 8.2130 8.22 0.1 4.8 9.3 50/50 3.4481 5.9082 5.97 1.0 function (di) has to be determined for each response Yi 4.8 9.3 24/76 3.4981 5.9086 5.99 1.4 (lnUCS, lnslump, lncost, %solid). The desirability (di) may 4.8 9.3 50/50 3.4481 5.9077 5.97 1.0 range from zero to one. A desirability of zero indicates average error: <1% 2.8 8.5 35/65 3.4981 81.2 82 1.0 least desirable value of Yi ; this represents a property 6.8 8.5 35/65 3.4981 65 64.5 0.8 level that expected to render the product (paste backfill) 6.8 8.5 65/35 3.4271 65 65.1 0.1 unacceptable for use. A desirability of one indicates most 2.8 10 65/35 3.4981 78.6 77.4 1.5 desirable or ideal value of Yi. The individual desirabilities %Solid 2.8 10 65/35 3.4271 78.6 78 0.8 (di) are then combined using the geometric mean, which 6.8 10 65/35 3.4271 61 60.5 0.9 gives the overall desirability D. The overall desirability 4.8 9.3 50/50 3.4481 70.3 70.8 0.8 function is defined by 4.8 9.3 24/76 3.4981 70.2 70.9 0.9 4.8 7.9 50/50 3.4481 73.5 74.9 1.9 average error: 1% 1 *Cem.: %cement; %Fi.: %Fine; Err.: error; Expe.: experimental; q å ri r Pred.: predicted D = (Õ d i ) (3) i i =1 5. OPTIMIZATION The aim of this optimization is to find optimal paste backfill where di, are individual desirability, ri is a value between mixes that allow to produce cost-effective (high quality) one and five reflecting the relative importance of response paste backfill. This means, the backfill produced in the Yi. plant must simultaneous satisfy several performance criteria. These criteria are described below: For example, if Yi is specified to be in some target range - Stability criteria; the paste backfill must remain stable (Li, Ui), with target value Ti, then di, the desirability during the extraction of neighbouring stopes in order to corresponding to Yi is defined by ensure the security of the mine workers. This means, the UCS 28 days (short term) of the backfill is to be higher than 700 kPa (Hassani and Bois, 1992). The d i = 0, Yi < Li , (4) long term strength (UCS > 90 days) of the backfill was not considered. Because of the low sulphate content of the backfill (< 500 ppm), there can not be a strength Yi - Li a loss due to sulphate attack. di = ( ) , Li £ Yi £ Ti (5) - Transportability criteria; the paste backfill has to be Ti - Li transported and then pumped to underground. This means, the produced backfill must have a technical Yi - U i b acceptable consistency. This consistency is described di = ( ) , Ti £ Yi £ U i (6) in terms of its slump. After Landriault et al. (1997), to Ti - U i ensure the ability of the produced paste backfill to be pumped to underground, its slump has to be between 15 and 25 cm. d i = 0, Yi > U i , (7) - Economical criteria; an essential requirement is that the paste backfill must be of low cost, i.e. to reduce the binder consumption at the maximum without affecting where a and b determining how important it is to hit the the others performance criteria of the paste backfill. target value. For example, for 28-day strength, the Because the cement can represent up to 75% of the desirability value is 0 below 700 kPa (risk of backfill cemented backfill cost (Grice, 1998). failure) and 1 above 1000 kPa (ideal strength). - Physical-environmental criteria; since the placement of backfill underground directly reduces the quantity of However, if we want to minimize a response Yi, then di, tailings to be disposed on surface (tailing may the desirability corresponding to Yi is defined by constitute a pollution source for the environment), the maximization of the solid concentration without affecting the other backfill properties will allow to return d i = 1, Yi > Ti , (8) the maximum quantity of mine wastes to the underground. Yi - U i b di = ( ) , Ti £ Yi £ U i (9) Ti - U i d i = 0, Yi > U i , (10) particularly on quadratic functions formed a suitable basis for the prediction of mechanical, physical, economical and rheological performance properties of paste backfill and the optimization of its production. The developed models For example the cost is to be minimized, the desirability have allowed to obtain valuable results regarding the value is 1 below 2.5 % binder content and 0 above 5.5% relationship between the physical and chemical properties binder content (backfill too expensive). of the components of the paste backfill and its The optimum paste backfill mix was considered here as performance, the prediction of its strength. The results of that mix which offers the mine workers safe workplace this modelling are in perfect concordance with the results (700 <28-day strength<1000, Hassani and Bois 1992), of the experimental studies carried out in this work (Fall & has a technical acceptable consistence (15 cm<slump>25 Benzaazoua 2003-a) and by several authors (Lamos & cm), has a high solid concentration (70<%solid<85) and Clark 1989, Landriault 1995, Naylor et al 1997, Archibald minimizes cost (binder cost). Table 5 shows the optimized et al. 1998, Ouellet et al. 1998; Bernier et al. 1999, responses and their desired ranges. Benzaazoua et al. 2000, etc.). The performed optimization has simultaneous taken into account several paste backfill Table 5. Optimized Responses and their desired ranges properties including transportability (slump), strength development (security of mine workers) and cost Desired range (profitability of the paste backfill technology) and also Responses allowed the development of cost-effective backfill mixes. UCS 28 days (kPa) 700 < Y1>1000 The results of this research represent a significant Slump (cm) 15 < Y2 >25 advance in paste backfill technology and will greatly Cost ($/t*) Y3 < 5 % Solid 70 < Y4> 85 contribute to better understanding the behaviours of paste *can $/tonne solid backfill. However, additional researches will be necessary in order to improve the accuracy of the developed Assuming equal importance (r1 = r2 = r3 = r4 = r5) for the response surface models, to develop predictive models four paste backfill properties (Y1 = UCS, Y2 = Slump, Y3 = for long term strength (UCS 90-days), to take account of Cost, Y4 = %Solid), overall desirability has been the effect of changing mineralogical characteristics of the calculated and desirability plots were constructed as a tailing material on paste backfill performance and to widen function of the paste backfill components (%cement, W/C, the field of validation of the developed models. Additional %Fine, ρt) using equation (3). Figure 13 shows the overall validation tests have also to be performed. All these desirability function (D) of the paste backfill plotted problems couldn’t be studied in the available time. against the cement content, the ratio W/C, the tailings However, researches on these problems and on in situ- grain size and density (only tailings density between 3.36 application of the developed models are actually carrying and 3.50 g/cm³ has been considered in this optimization). out at URSTM-UQAT. Some desirabilities are relatively high, and some are near zero. It is important to remember that, by definition, if a D value is greater than zero, the backfill mix is acceptable. ACKNOWLEDGMENTS In figure 13, it is clear the quality of the paste backfill is mostly controlled by the cement content, the tailings grain The authors are grateful to IRSST (“Institut de Recherche size and density. Figure 13 clearly indicates that, for the Robert-Sauvé en santé et en Sécurité du Travail”) for given desirability curves and weight assignments, the financial supporting of this study, to all technicians and optimum mix is composed by 3.8 % binder content, W/C = chemists (particularly Hugues Bordeleau) of URSTM for 7, %Fine = 50%, ρt=3.46 cm³/g). However, a binder undertaking of the experimental analysis and tests. content of 3%, W/C =7, %Fine = 50%, ρt=3.46 cm³/g will also enable the backfill mix to satisfy all performances criteria mentioned above. REFERENCES Archibald, J. F., Chew, J. L. and Lausch, P. (1998). 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