Optimization of Parameters for Rheological Properties and Strength of Cemented Paste Backﬁll Blended with Coarse Aggregates

: Cemented paste backﬁll (CPB) technology is widely used for environmental protection and underground goaf treatment. The inﬂuences of solid concentration, coarse aggregates dosage, and cement dosage on the rheological properties and compressive strength of CPB blended with coarse aggregates (CA-CPB) are investigated through three-factor and four-level orthogonal experiments. The dynamic shear stress and plastic viscosity are selected to characterize the rheological properties of CA-CPB. The uniaxial compressive strength (UCS) is used to describe the compressive strength. The effect of each factor on rheological properties is different from that on UCS. The most signiﬁcant inﬂuences on rheological properties and UCS are solid concentration and cement dosage, respectively. The optimal levels of each factor for rheological properties and UCS are different, resulting in different optimal combinations obtained through range analysis. Therefore, the overall desirability function approach is employed to perform multiple response optimization. The optimal parameters for high ﬂuidity and strength obtained provide valuable information for the CA-CPB process in the Chifeng Baiyinnuoer Lead and Zinc Mine.


Introduction
Tailings generated during the ore processing and waste rock are the main solid wastes in the mining industry [1,2].Cemented paste backfill (CPB) technology is widely used for environmental protection and underground goaf treatment [3].In the CPB process, lowconcentration tailings' slurry is thickened and dewatered to a high-concentration slurry, and then mixed with cement to prepare a paste with non-stratification, non-segregation, and non-bleeding.After transportation to goaf through pipelines, paste slurry will be solidified to a filling-body to support goaf proof.With CPB technology, solid waste (tailings) is used to deal with the two major hazard sources (tailings dam and goaf), which is called "one waste to cure two harms" [3][4][5].
Moreover, some studies show that coarse aggregates (CAs) play an essential role in determining the rheological properties of fluid-solid mixtures such as concrete and debris flows [35,36].The CAs affect the yield stress through the effective volumetric solid concentration, which can be refined by the size, shape, PSD, and concentration of CAs [35].It was also found that the rheological properties of the concrete and lubrication layer highly depend on the size of CAs when concrete is being pumped [37].At the same time, the strength of concrete is greatly influenced by the CAs, including the content, size, surface morphology, structure, and mineralogical component of the CAs [38][39][40].
Inspired by the above works, waste rocks were used as coarse aggregates to adjust the rheological properties and compressive strength of CPB.We investigated the influence of solid (tailings, CAs, and cement) concentration (SC), CAs dosage (CAsD), and cement dosage (CD) on the rheological properties and compressive strength of CPB blended with coarse aggregates (CA-CPB).Moreover, we optimized parameters for the rheological properties and compressive strength of CA-CPB.
The rest of this paper is structured as follows.In Section 2, the materials and methods, including the properties of the solid materials (tailings, CAs, and cement), methods of the rheological properties test and uniaxial compressive strength (UCS) test, orthogonal experiment design, and test procedure, are introduced.The overall performance, range analysis, and multiple response optimization are shown and discussed in Section 3. In Section 4, we draw conclusions based on the results and discussions.

Materials
The tailings were sampled from the Chifeng Baiyinnuoer Lead and Zinc Mine located in the northeast of China.The waste rocks sampled from the same deposit were used as CAs.The commercial ordinary portland cement 42.5 (P.O.42.5) provided by Zhongshan Group, Zibo, China, was used as the binder.The density, bulk density, and tapped density of tailings, CAs, and cement are shown in Table 1.The PSDs of the tailings and cement analyzed by laser diffraction (TopSizer, OMEC, Zhuhai, China) are shown in Figure 1.The amounts of the tailings and cement <200 µm are 85.94% and 95.48%, respectively.The PSD of the CAs tested through the sieving method is given in Table 2.The PSD of the CAs were mainly in the range of 2500 µm to 10,000 µm.The amount of 8000-10,000 µm CAs content is about 55.69%.The chemical composition analysis of the tailings, CAs, and cement was performed by X-Ray Fluorescence (XRF).The results are given in Table 3.The main components of the solid materials were SiO2, CaO, MgO, Al2O3, and Fe2O3.

Test/Methods
An ICAR rheometer (Germann Instruments) was used to test the rheological parameters of CA-CPB.The ICAR rheometer consists of a container, a motor drive with a torque meter unit, and a four-bladed vane.A laptop computer with ICAR Rheometer software installed was applied to operate the driver, record the torque during the test, and calculate the rheological parameters.The operation and procedure of determining the rheologica properties have been explained in other studies [41][42][43].
The UCS test was performed on an automatic compression testing machine (Mode HYE-100) of the capacity 100 kN on 70.7 mm CA-CPB cube specimens.The loading rate was 0.2 kN s −1 and the presented results are the average of three specimens.

Orthogonal Experiment Design
The SC, CAsD, and CD were selected as the factors for the rheological properties and  The chemical composition analysis of the tailings, CAs, and cement was performed by X-Ray Fluorescence (XRF).The results are given in Table 3.The main components of the solid materials were SiO 2 , CaO, MgO, Al 2 O 3 , and Fe 2 O 3 .

Test/Methods
An ICAR rheometer (Germann Instruments) was used to test the rheological parameters of CA-CPB.The ICAR rheometer consists of a container, a motor drive with a torque meter unit, and a four-bladed vane.A laptop computer with ICAR Rheometer software installed was applied to operate the driver, record the torque during the test, and calculate the rheological parameters.The operation and procedure of determining the rheological properties have been explained in other studies [41][42][43].
The UCS test was performed on an automatic compression testing machine (Model HYE-100) of the capacity 100 kN on 70.7 mm CA-CPB cube specimens.The loading rate was 0.2 kN s −1 and the presented results are the average of three specimens.

Orthogonal Experiment Design
The SC, CAsD, and CD were selected as the factors for the rheological properties and compressive strength of CA-CPB.Specifically, SC is the mass fraction of the solid materials in CA-CPB, CAsD is the mass ratio of CAs to tailings, and the CD represents the mass ratio of cement to the sum of tailings and CAs.The dynamic shear stress (τ 0 ) and plastic viscosity (µ) were selected to characterize the rheological properties of CA-CPB.The UCSs of the CA-CPB after curing, 3 d, 7 d, 14 d, and 28 d, were used to describe the compressive strength of CA-CPB.
The orthogonal design method is widely applied to analyze multi-factor and multilevel cases using a normalized orthogonal table [44,45].Here, we employed an orthogonal table represented by the symbol L n (r m ) in this paper, where L stands for Latin square.Here, we recalled that an orthogonal table is a matrix whose number of columns m is that of factors, each of which can assume one of r different levels (level 1 to level r).The number of rows n and the entries of the table, which correspond to numbers between 1 and r, are chosen in such a way that for any choice of t columns, each t-tuple of levels {1,. . ., r } appears in exactly one row in the orthogonal table.The parameter t is usually called the strength of the orthogonal table.In our case, we have m = 3 factors of r = 4 different levels each along with t = 2.This gives rise to n = r t = 16 rows or experimental runs.Note that this number compares favorably with the theoretically possible number 4 3 = 64 of all possible combinations of all levels of all factors.We, here, used the L 16 ( 43 ) table as shown in Table 4.The level distributions for SC (%) was 77 (level 1), 78 (level 2), 80 (level 3), and 81 (level 4); for CAsD (%) was 5 (level 1), 10 (level 2), 15 (level 3), and 20 (level 4); and for CD was 1:10 (level 1), 1:8 (level 2), 1:6 (level 3), and 1:4 (level 4).
In each experiment, the test procedure was conducted, as shown in Figure 2. The solid materials were first mixed with tap water to make a CA-CPB slurry according to the values of SC, CAs, CD in Table 4.Then, the rheological properties test of fresh CA-CPB was conducted by the ICAR Rheometer.After the rheology test, the CA-CPB slurry was filled into 70.7 mm × 70.7 mm × 70.7 mm standard tri-molds and the molds were removed after about one day (24 h).Then, the CA-CPB specimens were cured for 2 days, 6 days, 13 days, and 27 days.The curing temperature was 20 • C and the relative humidity was controlled at 90(±2)%.Eventually, the UCS test was performed on a compression testing machine.

Overall Performance
The experimental results of the rheological properties and UCS tests through the orthogonal experiment design are shown in Table 5 as well as Figures 3 and 4. The value in

Overall Performance
The experimental results of the rheological properties and UCS tests through the orthogonal experiment design are shown in Table 5 as well as Figures 3 and 4. The value in parentheses after each property in Table 5 is the corresponding coefficient of variation, defined as the ratio of the standard deviation and the average of three specimens [46,47].
Table 5 and Figure 3 illustrate that the rheological properties and UCS of CA-CPB in any experiment are different from those of others.At the same time, τ 0 and µ are in the range of 43.355 to 392.993 Pa and 0.215 to 2.296 Pa s, respectively.
Moreover, Table 5 and Figure 4 show that the UCS of CA-CPB increases over the curing time in each experiment.The evolutions of 3 d UCS, 7 d UCS, 14 d UCS, and 28 d UCS over the curing time are in the same trend.

Range Analysis of Rheological Properties
Range analysis is widely utilized to evaluate the influence of each factor and obtain the optimal combination [48][49][50][51][52].In the procedure of range analysis, the range value Taking y1 (τ0) as an example, is the mean of the four values of τ0 with the same level 1 of factor A. It can be found from Table 2 that the four values are 43.355,74.320

Range Analysis of Rheological Properties
Range analysis is widely utilized to evaluate the influence of each factor and obtain the optimal combination [48][49][50][51][52].In the procedure of range analysis, the range value ( Taking y1 (τ0) as an example, is the mean of the four values of τ0 with the same level 1 of factor A. It can be found from Table 2 that the four values are 43.355,74.320,

Range Analysis of Rheological Properties
Range analysis is widely utilized to evaluate the influence of each factor and obtain the optimal combination [48][49][50][51][52].In the procedure of range analysis, the range value (R y i −m ) is calculated through Equation (1).
where R y i −m is the range value of the response y i under the effect of factor m. The subscript y 1 , y 2 , . . ., y 6 represent the six responses τ 0 , µ, 3 d CUS, 7 d CUS, 14 d CUS, and 28 d CUS, respectively.The subscript m is the factors A (SC), B (CAdS), and C (CD).At the same time, K y i −mr is the mean of the four responses y i with the same level r (r = 1, 2, 3, and 4) of factor m.
According to the value of R y i −m , we can determine the importance of each factor on the response y i .If the R y i −m value of factor m is bigger than any other factor, factor m has the most significant influence on the response y i .
Taking y 1 (τ 0 ) as an example, K τ 0 −A1 is the mean of the four values of τ 0 with the same level 1 of factor A. It can be found from Table 2 that the four values are 43.355,74.320, 89.974, and 112.011.Accordingly, K τ 0 −A1 is 79.91.Similarly, K τ 0 −A2 , K τ 0 −A3 , and K τ 0 −A4 are 131.60,239.08, and 279.68, respectively.Then R τ 0 −A can be obtained as 199.77, which is 279.68 minus 79.91.The relation curve of τ 0 with SC is shown in Figure 5a, which illustrates that the mean of τ 0 increases with the increase of SC.This knowledge is well-known in other studies [11,53].
Similarly, the values of R τ 0 −B and R τ 0 −C are 76.11 and 85.90, respectively.Considering R τ 0 −A is the largest among the three range values, A (SC) has the most significant influence on τ 0 .The degree of effect of the factors on τ 0 is A > C > B. The relation curves of τ 0 with A, B, and C are shown in Figure 5.Both the relationships between τ 0 and both A and C are positively linear.On the contrary, the relationship between τ 0 and both A and C is negatively linear.Lower yield stress means higher fluidity, thus the optimal levels of A, B, and C are 1, 4, and 1.Therefore, the optimal combination for τ 0 of CA-CPB is A1C1B4, in which A1, C1, and B4 represent level 1 of A, level of C, and level 4 of B, respectively.
Moreover, Figure 5 demonstrates that the relationships between µ and each factor are similar to those between τ 0 and each factor.The values of R µ−A , R µ−B , and R µ−C are 1.2095, 0.6340, and 0.4847, indicating that the order of the significant influence of each factor on µ is A > B > C. The optimal levels of A, B, and C are 1, 4, and 1, notably the same with τ 0 .The optimal combination for µ is A1B4C1.
trates that the mean of τ0 increases with the increase of SC.This knowledge is well-known in other studies [11,53].
Similarly  5.Both the relationships between τ0 and both A and C are positively linear.On the contrary, the relationship between τ0 and both A and C is negatively linear.Lower yield stress means higher fluidity, thus the optimal levels of A, B, and C are 1, 4, and 1.Therefore, the optimal combination for τ0 of CA-CPB is A1C1B4, in which A1, C1, and B4 represent level 1 of A, level of C, and level 4 of B, respectively.
Moreover, Figure 5 demonstrates that the relationships between μ and each factor are similar to those between τ0 and each factor.The values of 1.2095, 0.6340, and 0.4847, indicating that the order of the significant influence of each factor on μ is A > B > C. The optimal levels of A, B, and C are 1, 4, and 1, notably the same with τ0.The optimal combination for μ is A1B4C1.The rheological behaviors of CA-CPB under different SCs and CDs are similar to those of the pure CPB, which were investigated in other studies [11,13].For CPB, τ0 and μ decrease with the specific surface area [14].The specific surface area of CAs is smaller than that of the tailings, thus the increase of CAsD reduces the water holding capacity of CA-CPB.That is to say, a higher dosage of CAs leads to more free water in the CA-CPB, which increases fluidity.Therefore, the dosage of CAs is beneficial for CA-CPB in this study.

Range Analysis of UCS
According to the range analysis procedure, the relation curves of 3 d UCS, 7 d UCS, 14 d UCS, and 28 d UCS with A (SC), B (CAdS), and C (CD) are shown in Figure 6.
The UCS of CA-CPB obviously varied with all the three factors (SC, CAsD, and CD).tively.Therefore, the order of the significant influence of each factor on 3 d UCS is C > A > B. In the CPB process, high strength is always desirable.The optimal levels of A, B, and C are 4, 1, and 4, indicating that the optimal combination for 3 d UCS is C4A4B1.Similarly, the optimal combinations for 7 d UCS, 14 d UCS, and 28 d UCS are also C4A4B1.Moreover, Figure 6a demonstrates that the 3 d UCS first decreased with an increase in SC and then increased for SC > 78%.Additionally, the evolutions of 7 d UCS, 14 d UCS, and 28 d UCS with SC are similar to that of 3 d UCS.Normally, the UCS of CPB is positively correlated with SC [6,10].The first decrease of UCS in Figure 6a may be because of The rheological behaviors of CA-CPB under different SCs and CDs are similar to those of the pure CPB, which were investigated in other studies [11,13].For CPB, τ 0 and µ decrease with the specific surface area [14].The specific surface area of CAs is smaller than that of the tailings, thus the increase of CAsD reduces the water holding capacity of CA-CPB.That is to say, a higher dosage of CAs leads to more free water in the CA-CPB, which increases fluidity.Therefore, the dosage of CAs is beneficial for CA-CPB in this study.

Range Analysis of UCS
According to the range analysis procedure, the relation curves of 3 d UCS, 7 d UCS, 14 d UCS, and 28 d UCS with A (SC), B (CAdS), and C (CD) are shown in Figure 6.
The UCS of CA-CPB obviously varied with all the three factors (SC, CAsD, and CD).Concerning the 3 d UCS, the R 3d−A , R 3d−B , and R 3d−C are 0.675, 0.525, and 1.6, respectively.Therefore, the order of the significant influence of each factor on 3 d UCS is C > A > B. In the CPB process, high strength is always desirable.The optimal levels of A, B, and C are 4, 1, and 4, indicating that the optimal combination for 3 d UCS is C4A4B1.Similarly, the optimal combinations for 7 d UCS, 14 d UCS, and 28 d UCS are also C4A4B1.
Moreover, Figure 6a demonstrates that the 3 d UCS first decreased with an increase in SC and then increased for SC > 78%.Additionally, the evolutions of 7 d UCS, 14 d UCS, and 28 d UCS with SC are similar to that of 3 d UCS.Normally, the UCS of CPB is positively correlated with SC [6,10].The first decrease of UCS in Figure 6a may be because of the effect of CAs.Even though the impact of the CAsD on the UCS is the least significant, UCS first decreased with an increase in CAs and then increased for CAs > 15%, as shown in Figure 6b.Considering that not only the dosage but also the surface morphology and structure of CAs influence the UCS of concrete [54], the relation curves of the UCS of CA-CPB with CAsD are not monotonically increasing or decreasing.Moreover, UCS is mainly ascribed to the formed cementitious products (such as C-S-H gel) by hydration reactions, as the higher the CD, the more cementitious products are formed, resulting in higher UCS [55].The relationships between 3 d UCS and CD, 7 d UCS and CD, 14 d UCS and CD, and 28 d UCS and CD are almost positively linear in Figure 6c.The variation of the UCS of CA-CPB with CD is similar to that of pure CPB or other concretes [10,39,48,49].
structure of CAs influence the UCS of concrete [54], the relation curves of the UCS of CA-CPB with CAsD are not monotonically increasing or decreasing.Moreover, UCS is mainly ascribed to the formed cementitious products (such as C-S-H gel) by hydration reactions, as the higher the CD, the more cementitious products are formed, resulting in higher UCS [55].The relationships between 3 d UCS and CD, 7 d UCS and CD, 14 d UCS and CD, and 28 d UCS and CD are almost positively linear in Figure 6c.The variation of the UCS of CA-CPB with CD is similar to that of pure CPB or other concretes [10,39,48,49].

Multiple Response Optimization and Validation
Based on the above range analysis, the evolutions of the rheological properties with each factor are different from that of UCS.More seriously, the effect of each factor on the rheological properties is different to that on UCS.The optimal levels of A and C for rheological properties are 1 and 1, whereas that for UCS is 4. At the same time, the optimal level of B for the rheological properties is 4, but that for UCS is 1.The optimal levels of each factor for the rheological properties and UCS are different, resulting in different optimal combinations.It is difficult to achieve the highest UCS and highest fluidity (lowest τ0 and μ) simultaneously.At the same time, the variations in 3 d UCS, 7 d UCS, 14 d UCS, and 28 d UCS with each factor are similar.
Therefore, τ0, μ, and 28 d UCS were selected as the responses for optimizing rheological properties and UCS.The multiple response optimization was conducted through the overall desirability (OD) function approach, which has been employed in other studies [56,57].Then, the optimal conditions for multiple responses were obtained by maximizing the OD function, as shown in Equation (2).
( ) where d1, d2, and d6 represent an individual desirability function-converted response y1, y2, and y6, respectively.The scale of d1, d2, and d6 ranges from 0 to 1 to the possible values of y1, y2, and y6, where 0 represents that the response is fully unacceptable and 1 illustrates that the response is fully desirable.The individual desirability functions of d1, d2, and d6 are given in Equations ( 3)-( 5).

Multiple Response Optimization and Validation
Based on the above range analysis, the evolutions of the rheological properties with each factor are different from that of UCS.More seriously, the effect of each factor on the rheological properties is different to that on UCS.The optimal levels of A and C for rheological properties are 1 and 1, whereas that for UCS is 4. At the same time, the optimal level of B for the rheological properties is 4, but that for UCS is 1.The optimal levels of each factor for the rheological properties and UCS are different, resulting in different optimal combinations.It is difficult to achieve the highest UCS and highest fluidity (lowest τ 0 and µ) simultaneously.At the same time, the variations in 3 d UCS, 7 d UCS, 14 d UCS, and 28 d UCS with each factor are similar.
Therefore, τ 0 , µ, and 28 d UCS were selected as the responses for optimizing rheological properties and UCS.The multiple response optimization was conducted through the overall desirability (OD) function approach, which has been employed in other studies [56,57].Then, the optimal conditions for multiple responses were obtained by maximizing the OD function, as shown in Equation (2).
where d 1 , d 2 , and d 6 represent an individual desirability function-converted response y 1 , y 2 , and y 6 , respectively.The scale of d 1 , d 2 , and d 6 ranges from 0 to 1 to the possible values of y 1 , y 2 , and y 6 , where 0 represents that the response is fully unacceptable and 1 illustrates that the response is fully desirable.The individual desirability functions of d 1 , d 2 , and d 6 are given in Equations ( 3)-( 5).

Figure 3 .Figure 4 .
Figure 3. Variation in rheological properties of the orthogonal experiment.

3 and 4 )
value of the response yi under the effect of factor m. The sub script y1, y2,…, y6 represent the six responses τ0, μ, 3 d CUS, 7 d CUS, 14 d CUS, and 28 d CUS, respectively.The subscript m is the factors A (SC), B (CAdS), and C (CD).At the same time, of the four responses yi with the same level r (r = 1, 2, of factor m. According to the value of − i y m R , we can determine the importance of each factor on the response yi.If the m is bigger than any other factor, factor m ha the most significant influence on the response yi.

Figure 3 .
Figure 3. Variation in rheological properties of the orthogonal experiment.

Figure 3 .
Figure 3. Variation in rheological properties of the orthogonal experiment.

Figure 4 .
Figure 4. Variation in UCS of the orthogonal experiment.
value of the response yi under the effect of factor m. The subscript y1, y2,…, y6 represent the six responses τ0, μ, 3 d CUS, 7 d CUS, 14 d CUS, and 28 d CUS, respectively.The subscript m is the factors A (SC), B (CAdS), and C (CD).At the same time, of the four responses yi with the same level r (r = 1m is bigger than any other factor, factor m has the most significant influence on the response yi.

Figure 4 .
Figure 4. Variation in UCS of the orthogonal experiment.
among the three range values, A (SC) has the most significant influence on τ0.The degree of effect of the factors on τ0 is A > C > B. The relation curves of τ0 with A, B, and C are shown in Figure

Table 1 .
Density, bulk density, and tapped density of solid materials.

Table 2 .
PSD of the coarse aggregates.

Table 2 .
PSD of the coarse aggregates.

Table 3 .
Chemical components of solid materials.

Table 5 .
Experimental results of rheological properties and UCS tests.