# Analysis of Influencing Factors of Cementitious Material Properties of Lead–Zinc Tailings Based on Orthogonal Tests

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Test Method

#### 2.1. Test Materials

_{10}and d

_{60}, the inhomogeneity coefficient Cu = d

_{60}/d

_{10}= 15.297 ≥ 5 [41], thus it is well graded and easily mixed and reacted to make cementitious materials. The market price of primary fly ash is 17.244 USD/ton, with a chemical composition similar to clay and a fine particle size. The cement is 425 ordinary silicate cement, whose market price is 54.606 USD/ton. The chemical composition of fly ash and cement is shown in Table 1 [42], and the particle size of river sand was chosen to be uniform and reasonable, with rounded particles, smooth surface, and good fluidity.

_{2}, Fe

_{2}O

_{3}, Al

_{2}O

_{3}, CaO, and MgO, of which the SiO

_{2}content can reach 48.17%. From Table 1 and Table 2, it can be seen that both Pb–Zn tailings and fly ash contain more SiO

_{2}compared to cement, therefore, the increase of Pb–Zn tailings and fly ash content is beneficial to the formation of the cementitious material skeleton and improves the denseness of the material. In addition, more active ingredients such as CaO and Al

_{2}O

_{3}in cement and fly ash can maintain the activity of cementitious materials and enhance the cementation of materials [43,44].

#### 2.2. Test Design

_{16}(4

^{3}). Sixteen groups of this test were subjected to uniaxial compression test after 3 days, 7 days, and 28 days of maintenance. The factors and their levels corresponding to each group are shown in Table 3.

#### 2.3. Test Procedures

## 3. Results and Discussions

#### Compression Test Analysis

## 4. Response Surface Prediction Regression Analysis

#### 4.1. Regression Analysis

^{2}values of the complex correlation coefficients of the regression equations are all greater than 0.90, indicating that the equations fit well and can predict the strength of the filler at each age more accurately [63,64,65]; the three different maintenance period strength results in the regression equation, the p value response of the ABC three factors, is the degree of influence on compressive strength. From Table 6, Table 7 and Table 8, it can be seen that all three factors have a significant effect on the compressive strength. The errors between the predicted and actual values of the compressive strength equation of the cementitious material are shown in Table 9. To show the relationship between actual and predicted values more visually, Table 9 was transformed into the one shown in Figure 7. From Figure 7, it is clear that the predicted values of compressive strength of the gelling material are close to the actual values on the y = x straight line, which further proves that this regression equation fits well.

#### 4.2. Optimized Ratios

## 5. Conclusions

- (1)
- The lead–zinc tailings are well graded and contain mainly quartz, mica, dolomite, chlorite, and other mineral components. The main chemical components are Fe
_{2}O_{3}, SiO_{2}, Al_{2}O_{3}, MgO, CaO, etc. - (2)
- The sensitivity of each factor to strength at 3 days of age is water–binder ratio > lead–zinc tailings content > fly ash content; The sensitivity of each factor to strength at 7 days of age is fly ash content > lead–zinc tailings content > water–binder ratio; The sensitivity of each factor to strength at the age of 28 days is water–binder ratio > lead–zinc tailings content > fly ash content. For specimens under a short curing period (3 d), the most powerful sensitivity parameter is water–binder ratio. The best curing period for specimens is 28 d. With sufficient hydration, the strength is significantly higher than that of the specimen with curing periods of 3 d and 7 d.
- (3)
- For the comprehensive realistic price factors and compressive strength requirements of cementitious materials in the known test group, a water–binder ratio of 0.4 is chosen for the 28-day age cementitious material, and the ratio of fly ash:lead–zinc tailings:cement = 30:40:60, when the valence ratio is 0.38 USD/MPa. In the equation prediction, fly ash:lead–zinc tailings:cement = 30:40:30, with the water–binder ratio of 0.4 is the optimal ratio, when the compressive strength can reach 22.281 MPa.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**The change diagram of compressive strength at 3 days, 7 days, and 28 days curing of each factor.

**Figure 7.**Comparison of predicted and actual values of compressive strength for different curing days.

Material | Chemical Compositions (%) | |||||||
---|---|---|---|---|---|---|---|---|

Na_{2}O | SiO_{2} | Al_{2}O_{3} | MgO | CaO | P_{2}O_{5} | K_{2}O | Fe_{2}O_{3} | |

Fly Ash | 1.670 | 48.800 | 26.260 | 1.840 | 4.951 | 0.146 | 2.000 | 4.869 |

Cement | 0.276 | 14.240 | 5.410 | 1.799 | 52.84 | 0.408 | 0.892 | 2.461 |

Material | Chemical Compositions (%) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

TFe | SiO_{2} | Al_{2}O_{3} | MgO | CaO | K_{2}O | MnO_{2} | TiO_{2} | Na_{2}O | ZnO | Other | |

Lead–Zine Tailings | 14.15 | 48.17 | 10.79 | 4.14 | 4.20 | 3.01 | 0.73 | 0.31 | 0.46 | 0.49 | 13.55 |

Sample No. | Fly Ash/% | Lead–Zinc Tailings/% | Cement/% | Water–Binder Ratio |
---|---|---|---|---|

1 | 15 | 25 | 60 | 0.4 |

2 | 15 | 30 | 55 | 0.45 |

3 | 15 | 35 | 50 | 0.5 |

4 | 15 | 40 | 45 | 0.55 |

5 | 20 | 25 | 55 | 0.55 |

6 | 20 | 30 | 50 | 0.4 |

7 | 20 | 35 | 45 | 0.45 |

8 | 20 | 40 | 40 | 0.5 |

9 | 25 | 25 | 50 | 0.5 |

10 | 25 | 30 | 45 | 0.55 |

11 | 25 | 35 | 40 | 0.4 |

12 | 25 | 40 | 35 | 0.45 |

13 | 30 | 25 | 45 | 0.45 |

14 | 30 | 30 | 40 | 0.5 |

15 | 30 | 35 | 35 | 0.55 |

16 | 30 | 40 | 30 | 0.4 |

Sample No. | 3 Days | 7 Days | 28 Days |
---|---|---|---|

1 | 14.04 | 22.04 | 36.92 |

2 | 11.58 | 17.46 | 22.27 |

3 | 8.55 | 13.66 | 21.81 |

4 | 5.3 | 8.5 | 12.16 |

5 | 7.09 | 12.22 | 20.55 |

6 | 10.34 | 15.13 | 21.76 |

7 | 6.39 | 10.71 | 17.36 |

8 | 4.21 | 6.01 | 12.82 |

9 | 8.44 | 13.08 | 23.65 |

10 | 5.29 | 7.85 | 15.41 |

11 | 6.02 | 9.44 | 17.91 |

12 | 4.52 | 6.45 | 13.16 |

13 | 7.71 | 9.22 | 19.25 |

14 | 5.31 | 7.47 | 12.56 |

15 | 3 | 5.08 | 10.59 |

16 | 7.39 | 11.24 | 22.91 |

Mean value | 7.20 | 10.97 | 18.82 |

Standard deviation | 2.81 | 4.39 | 6.30 |

Levels | Lead–Zine Tailings (%) | Fly Ash(%) | Water–Binder Ratio |
---|---|---|---|

1 | 25 | 15 | 0.40 |

2 | 30 | 20 | 0.45 |

3 | 35 | 25 | 0.50 |

4 | 40 | 30 | 0.55 |

Source of Variation | Mean Square | Degrees of Freedom | Quadratic Sum | Value p |
---|---|---|---|---|

Model | 63.05 | 7 | 9.01 | 0.0328 |

A | 21.17 | 1 | 21.17 | 0.0129 |

B | 14.36 | 1 | 14.36 | 0.0244 |

C | 25.35 | 1 | 25.35 | 0.0094 |

AC | 0.91 | 1 | 0.91 | 0.4259 |

BC | 2.19 | 1 | 2.19 | 0.2407 |

A^{2} | 6.55 | 1 | 6.55 | 0.0760 |

B^{2} | 0.56 | 1 | 0.56 | 0.5247 |

Residual | 4.63 | 4 | 1.16 | |

SUM | 67.68 | 11 |

Source of Variation | Mean Square | Degrees of Freedom | Quadratic Sum | Value p |
---|---|---|---|---|

Model | 140.84 | 6 | 23.47 | 0.0114 |

A | 71.81 | 1 | 71.81 | 0.0026 |

B | 54.05 | 1 | 54.05 | 0.0048 |

C | 26.96 | 1 | 26.96 | 0.0193 |

AB | 16.61 | 1 | 16.61 | 0.0446 |

AC | 1.12 | 1 | 1.12 | 0.5190 |

A^{2} | 7.97 | 1 | 7.97 | 0.1241 |

Residual | 11.69 | 5 | 2.34 | |

SUM | 152.53 | 11 | 0.0114 |

Source of Variation | Mean Square | Degrees of Freedom | Quadratic Sum | Value p |
---|---|---|---|---|

Model | 208.41 | 6 | 34.74 | 0.0214 |

A | 54.38 | 1 | 54.38 | 0.0186 |

B | 59.47 | 1 | 59.47 | 0.0157 |

C | 3.53 | 1 | 3.53 | 0.4218 |

BC | 27.52 | 1 | 27.52 | 0.0586 |

B^{2} | 11.61 | 1 | 11.61 | 0.1737 |

B^{2}C | 20.44 | 1 | 20.44 | 0.0893 |

Residual | 23.09 | 5 | 4.62 | |

SUM | 231.50 | 11 |

3 Day Age/MPa | 7 Day Age/MPa | 28 Day Age/MPa | |||||||
---|---|---|---|---|---|---|---|---|---|

Test Group Number | Actual Value | Predicted Value | Error Magnitude | Actual Value | Predicted Value | Error Magnitude | Actual Value | Predicted Value | Error Magnitude |

1 | 14.04 | 14.42 | 0.38 | 22.04 | 22.38 | 0.34 | 36.92 | 34.72 | −2.2 |

7 | 6.39 | 6.50 | 0.11 | 10.71 | 10.12 | −0.59 | 17.36 | 17.15 | −0.21 |

12 | 4.52 | 4.31 | −0.21 | 6.45 | 6.66 | 0.21 | 13.16 | 13.85 | 0.69 |

14 | 5.31 | 5.68 | 0.37 | 7.47 | 7.00 | −0.47 | 12.56 | 13.36 | 0.8 |

Test Group Number | Test Cost (USD/ton) | 3 d Price Ratio (USD/MPa) | 7 d Price Ratio (USD/MPa) | 28 d Price Ratio (USD/MPa) |
---|---|---|---|---|

1 | 14.14 | 1.01 | 0.64 | 0.38 |

2 | 15.91 | 1.37 | 0.91 | 0.71 |

3 | 17.68 | 2.07 | 1.29 | 0.81 |

4 | 19.44 | 3.67 | 2.29 | Strength does not match |

5 | 19.44 | 2.74 | 1.59 | 0.95 |

6 | 14.14 | 1.37 | 0.93 | 0.65 |

7 | 15.91 | 2.49 | 1.49 | Strength does not match |

8 | 17.68 | 4.20 | 2.94 | Strength does not match |

9 | 17.68 | 2.09 | 1.35 | 0.75 |

10 | 19.44 | 3.68 | 2.48 | Strength does not match |

11 | 14.14 | 2.35 | 1.50 | Strength does not match |

12 | 15.91 | 3.52 | 2.47 | Strength does not match |

13 | 15.91 | 2.06 | 1.73 | Strength does not match |

14 | 17.68 | 3.33 | 2.37 | Strength does not match |

15 | 19.44 | Strength does not match | 3.83 | Strength does not match |

16 | 14.14 | 1.91 | 1.26 | 0.62 |

Strength | Grade | Compressive Strength | |
---|---|---|---|

General mortar strength | 3 d | 28 d | |

I | ≥4.0 | ≥20.0 |

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## Share and Cite

**MDPI and ACS Style**

Yin, Z.; Li, R.; Lin, H.; Chen, Y.; Wang, Y.; Zhao, Y. Analysis of Influencing Factors of Cementitious Material Properties of Lead–Zinc Tailings Based on Orthogonal Tests. *Materials* **2023**, *16*, 361.
https://doi.org/10.3390/ma16010361

**AMA Style**

Yin Z, Li R, Lin H, Chen Y, Wang Y, Zhao Y. Analysis of Influencing Factors of Cementitious Material Properties of Lead–Zinc Tailings Based on Orthogonal Tests. *Materials*. 2023; 16(1):361.
https://doi.org/10.3390/ma16010361

**Chicago/Turabian Style**

Yin, Ziyi, Rui Li, Hang Lin, Yifan Chen, Yixian Wang, and Yanlin Zhao. 2023. "Analysis of Influencing Factors of Cementitious Material Properties of Lead–Zinc Tailings Based on Orthogonal Tests" *Materials* 16, no. 1: 361.
https://doi.org/10.3390/ma16010361