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

^{1}

^{2}

^{3}

^{2}MA and Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción 4070371, Chile

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

_{2}, CaO, MgO, Al

_{2}O

_{3}, and Fe

_{2}O

_{3}.

#### 2.2. Test/Methods

^{−1}and the presented results are the average of three specimens.

#### 2.3. Orthogonal Experiment Design

_{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.

_{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}(4

^{3}) 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).

## 3. Results and Discussion

#### 3.1. Overall Performance

#### 3.2. Range Analysis of Rheological Properties

_{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, $\overline{{K}_{{y}_{i}-mr}}$ is the mean of the four responses y

_{i}with the same level r (r = 1, 2, 3, and 4) of factor m.

_{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}.

_{1}(τ

_{0}) as an example, $\overline{{K}_{{\tau}_{0}-\mathrm{A}1}}$ 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, $\overline{{K}_{{\tau}_{0}-\mathrm{A}1}}$ is 79.91. Similarly, $\overline{{K}_{{\tau}_{0}-\mathrm{A}2}}$, $\overline{{K}_{{\tau}_{0}-\mathrm{A}3}}$, and $\overline{{K}_{{\tau}_{0}-\mathrm{A}4}}$ are 131.60, 239.08, and 279.68, respectively. Then ${R}_{{\tau}_{0}-\mathrm{A}}$ 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].

_{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.

_{0}and each factor. The values of ${R}_{\mu -\mathrm{A}}$, ${R}_{\mu -\mathrm{B}}$, and ${R}_{\mu -\mathrm{C}}$ 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.

_{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.

#### 3.3. Range Analysis of UCS

#### 3.4. Multiple Response Optimization and Validation

_{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.

_{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).

_{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.

_{1}, d

_{2}, and d

_{6}are given in Equations (3)–(5).

_{1}in Table 2 and 200 is the upper limit of τ

_{0}in CPB [58]. The values 0.215 and 2.296 are the minimum and maximum of y

_{2}in Table 2, respectively. The values 1.9 and 9.2 are the lower and upper limits of y

_{6}under the given experimental setup, respectively.

_{1}, y

_{2}, and y

_{6}in the form of a quadratic polynomial equation are shown in Equations (6)–(8).

_{0}= 85.129 Pa, μ= 0.469 Pa s, and 28 d UCS = 6.96 MPa.

_{0}= 91.606 Pa, μ= 0.482 Pa s, and 28 d UCS = 6.5 MPa. The relative errors between predicted and measured values are between −7% and 7% provided that the proposed models are feasible. The optimal parameters above could provide valuable information for the CA-CPB process in the Chifeng Baiyinnuoer Lead and Zinc Mine.

## 4. Conclusions

- (1)
- The effects of solid concentration, coarse aggregates dosage, and cement dosage on rheological properties differ from that on UCS. The most significant influences on rheological properties and UCS are solid concentration and cement dosage, respectively.
- (2)
- The optimal combinations for rheological properties and UCS are different.
- (3)
- The overall desirability function is an effective approach for multiple response optimization of CA-CPB.
- (4)
- The optimal conditions for the high fluidity and high strength of CA-CPB in this study are a solid concentration of 77%, coarse aggregates dosage of 20%, and cement dosage of 0.227, producing τ
_{0}of 85.129 Pa, μ of 0.469 Pa s, and 28 d UCS of 6.96 MPa.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CA-CPB | CPB blended with coarse aggregates |

CAs | coarse aggregates |

CAsD | CAs dosage |

CD | cement dosage |

CPB | cemented paste backfill |

OD | overall desirability |

PSD | particle size distribution |

SC | solid (tailings, CAs, and cement) concentration |

UCS | uniaxial compressive strength |

XRF | X-Ray Fluorescence |

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**Figure 5.**Relation curves of rheological properties with (

**a**) SC (solid concentration), (

**b**) CAsD (coarse aggregates dosage), and (

**c**) CD (cement dosage) by range analysis.

**Figure 6.**Relation curves of UCS with (

**a**) SC (solid concentration), (

**b**) CAsD (coarse aggregates dosage), and (

**c**) CD (cement dosage) by range analysis.

Materials | Density (g cm ^{−3}) | Bulk Density (g cm ^{−3}) | Tapped Density (g cm ^{−3}) |
---|---|---|---|

Tailings | 2.74 | 1.449 | 1.951 |

Coarse aggregates | 2.52 | 1.429 | 1.647 |

Cement | 3.09 | 1.022 | 1.384 |

Particle Size (μm) | Mass Content (%) |
---|---|

+8000–10,000 | 55.69 |

+7000–8000 | 14.83 |

+6000–7000 | 6.80 |

+5000–6000 | 8.87 |

+2500–5000 | 12.71 |

+1250–2500 | 0.32 |

+315–1250 | 0.06 |

−315 | 0.71 |

Chemical Component | SiO_{2}(%) | CaO (%) | MgO (%) | Al_{2}O_{3}(%) | Fe_{2}O_{3}(%) | SO_{3}(%) | K_{2}O(%) | TiO_{2}(%) | MnO (%) | Others (%) |
---|---|---|---|---|---|---|---|---|---|---|

Tailings | 39.18 | 35.89 | 3.49 | 6.99 | 10.23 | 0.19 | 1.28 | 0.32 | 2.42 | 0.01 |

Coarse aggregates | 23.51 | 59.00 | 2.41 | 5.56 | 7.11 | 0.35 | 1.20 | 0.33 | 0.51 | 0.02 |

Cement | 29.12 | 50.86 | 2.14 | 9.06 | 3.29 | 3.47 | 1.27 | 0.62 | 0.16 | 0.01 |

Experiment Number | Solid Concentration (%) | Coarse Aggregates Dosage (%) | Cement Dosage |
---|---|---|---|

1 | 77 (level 1) | 5 (level 1) | 1:10 (level 1) |

2 | 77 | 10 (level 2) | 1:8 (level 2) |

3 | 77 | 15 (level 3) | 1:6 (level 3) |

4 | 77 | 20 (level 4) | 1:4 (level 4) |

5 | 78 (level 2) | 5 | 1:8 |

6 | 78 | 10 | 1:10 |

7 | 78 | 15 | 1:4 |

8 | 78 | 20 | 1:6 |

9 | 80 (level 3) | 5 | 1:6 |

10 | 80 | 10 | 1:4 |

11 | 80 | 15 | 1:10 |

12 | 80 | 20 | 1:8 |

13 | 81 (level 4) | 5 | 1:4 |

14 | 81 | 10 | 1:6 |

15 | 81 | 15 | 1:8 |

16 | 81 | 20 | 1:10 |

Experiment Number | τ_{0} (Pa) | μ (Pa s) | 3 d UCS (MPa) | 7 d UCS (MPa) | 14 d UCS (MPa) | 28 d UCS (MPa) |
---|---|---|---|---|---|---|

1 | 43.36 (18.25) | 0.273 (19.97) | 0.5 (34.64) | 1 (34.64) | 1.8 (19.25) | 1.9 (9.12) |

2 | 74.32 (19.67) | 0.215 (25.14) | 0.6 (28.87) | 1.3 (13.32) | 2.4 (18.16) | 2.6 (10.18) |

3 | 89.97 (21.93) | 0.254 (18.98) | 1.1 (24.05) | 2.4 (4.17) | 3.5 (7.56) | 4.5 (5.88) |

4 | 112.01 (20.95) | 0.776 (17.65) | 2.6 (7.69) | 4.3 (8.39) | 6.4 (5.41) | 8.1 (2.14) |

5 | 191.54 (21.93) | 1.377 (30.03) | 0.9 (22.22) | 2.1 (12.60) | 3.3 (13.21) | 3.8 (6.96) |

6 | 136.89 (23.66) | 1.004 (26.39) | 0.6 (28.87) | 1 (20.00) | 1.8 (19.25) | 1.9 (9.12) |

7 | 112.21 (27.79) | 0.843 (22.87) | 1.5 (11.55) | 3.6 (7.35) | 5.5 (6.56) | 5.6 (4.72) |

8 | 85.78 (22.30) | 0.352 (29.77) | 1.2 (22.05) | 1.9 (13.93) | 3.6 (7.35) | 3.8 (9.12) |

9 | 266.66 (20.01) | 1.625 (28.18) | 1.4 (14.29) | 2.8 (9.45) | 5.7 (9.28) | 5.9 (5.87) |

10 | 299.80 (22.31) | 1.705 (28.17) | 2.1 (12.60) | 4.5 (2.22) | 6.5 (5.33) | 8.1 (2.14) |

11 | 195.34 (22.95) | 1.38 (24.55) | 0.6 (16.67) | 1.2 (22.05) | 2.3 (18.95) | 2.4 (14.43) |

12 | 194.52 (25.53) | 0.883 (27.06) | 0.8 (21.65) | 1.7 (11.76) | 2.7 (9.80) | 3.3 (8.02) |

13 | 392.99 (24.64) | 2.296 (22.03) | 2.9 (3.45) | 5.8 (4.56) | 8.5 (6.55) | 9.2 (1.09) |

14 | 299.06 (22.07) | 1.675 (31.96) | 1.7 (5.88) | 3.6 (7.35) | 5.3 (4.99) | 7.4 (3.58) |

15 | 228.89 (21.94) | 1.361 (28.26) | 1.1 (24.05) | 2.1 (12.60) | 3.7 (8.11) | 4.9 (3.53) |

16 | 197.81 (26.13) | 1.024 (22.63) | 0.6 (28.87) | 1.4 (12.37) | 2.4 (11.02) | 2.8 (3.57) |

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Wang, J.; Wu, A.; Ruan, Z.; Bürger, R.; Wang, Y.; Wang, S.; Zhang, P.; Gao, Z. Optimization of Parameters for Rheological Properties and Strength of Cemented Paste Backfill Blended with Coarse Aggregates. *Minerals* **2022**, *12*, 374.
https://doi.org/10.3390/min12030374

**AMA Style**

Wang J, Wu A, Ruan Z, Bürger R, Wang Y, Wang S, Zhang P, Gao Z. Optimization of Parameters for Rheological Properties and Strength of Cemented Paste Backfill Blended with Coarse Aggregates. *Minerals*. 2022; 12(3):374.
https://doi.org/10.3390/min12030374

**Chicago/Turabian Style**

Wang, Jiandong, Aixiang Wu, Zhuen Ruan, Raimund Bürger, Yiming Wang, Shaoyong Wang, Pingfa Zhang, and Zhaoquan Gao. 2022. "Optimization of Parameters for Rheological Properties and Strength of Cemented Paste Backfill Blended with Coarse Aggregates" *Minerals* 12, no. 3: 374.
https://doi.org/10.3390/min12030374