4TH JOINT IAH-CNC/CGS CONFERENCE                                                4ième CONFÉRENCE CONJOINTE AIH-CCN/SCG
2003 NAGS CONFERENCE                                                                             2003 NAGS CONFÉRENCE

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 :
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)
                                                                                                                                     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)

sulphate attack. The first type of models will be presented                                           70
in this paper. The second type of models is presented                                                 60
elsewhere (Fall & Benzaazoua, 2003-b). This paper will                                                                        23
be also focussed on the results of modeling and                                                                               80
optimization study. The results of the experimental study                                                                     25
are detailed described in the works of Benzaazoua et al.                                                                      30
2003, Fall & Benzaazoua 2003a.                                                                        20                      10
                                                                                                           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
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
terms xi represents second order non-linearity. The                  2
                                                                     r : coefficient of determination; r: adjusted coefficient of determination
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
     variables cement, W/C, % Fines, ρt. The square term                                                                       1100               40%
     x1 is also statistical significant.

                                                                                                                   UCS (kPa)
                                                                                                                               1000               45%
   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

   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,
   tailings grain size and density on lnUCS 28 days. As                                                                                                                                              % Cement
   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)

   ratio is mainly caused by the subsequent increasing in
   overall porosity due to the once water-filled voids                                                                              1000

   (Amaraunga & Yaschyshyn, 1997).


                     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)

                                  % ciment
                                                                                                 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 =
                                   W/C = 6
                                                                                                                   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
                                   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
                                                                                                                   (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
                                                                                                                   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 =
                                             ρt = 3.400                                                                                                              2,5 257

                                             ρt = 3.450                                                                                                                    3.1
                        1600                                                                                                                                      2,2 30424
                                             ρt = 3.500

                        1400                                                                                                                                         1,2 528
           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
                                                                                                                                                                                      % Cement
                                                                                                                                                                                       % cime nt
                                                                                                                                                                                                                                                 t (g/cm³)

                         600                                                                                                                                     Figure 11. Prediction profile of lnslump (slumo in cm)

                         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

                       1300                                                                                                 5                                    72.5

                       1200                                                                                                                                         58,5
                                                                                                                            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

                       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
                                                                                                                            3.5                                                  paste backfill
                                                                                                                            3                       4.2.3 Model validation
                                        UCS 28 days (kPa)
                                        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
                                                                                                                                                    well within the relative standard uncertainty of 5 to 10%
                                                                                                                                                    for the uniaxial compressible tests.

          1,7 61174

                       0,6 454
                                                                                                                                                    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
                                                                                                                                                                                 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         (%)

   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
 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%
           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
Pred.: predicted                                                    D = (Õ d i )                                             (3)
                                                                         i =1

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

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