Multi-Response Robust Parameter Optimization of Cemented Backfill Proportion with Ultra-Fine Tailings
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials
2.2. Orthogonal Experiment of Filling Proportion
2.3. RSM Experiment of Filling Proportion
2.4. Experimental Process
3. Results and Discussion
3.1. Influence of Single Factors on Backfill Strength and Slump
3.2. Interactive Influence of Multi-Factors on Backfill Strength and Slump
(R12= 0.9940)
(R22= 0.9945)
(R32= 0.9912)
3.3. Multi-Response Robust Optimization of Filling Proportion
- (1)
- Robust optimization of filling proportion
- (2)
- Multi-response robust optimization validation test
4. Conclusions
- To alleviate the low backfill strength and poor slurry fluidity of Carlin-type gold deposits with ultra-fine tailings, orthogonal experiments and the RSM method were used to reveal the influence of variable factors and their interaction on backfill strength and slurry slump. The influential factor sequence of backfill unconfined compressive strength at each curing age was the cement-sand ratio > slurry mass concentration > waste rock content. Backfill slurry slump was sequentially influenced by slurry mass concentration > waste rock content > cement-sand ratio.
- The interactive influence of multi-factors on the backfill strength and slump was studied by constructing a response surface with slurry mass concentration, waste rock content and cement-sand ratio. The results showed that the interaction between slurry mass concentration and cement-sand ratio has a positive correlation with backfill strength. The interaction between slurry mass concentration and cement-sand ratio, as well as the interaction between slurry mass concentration and waste rock content, contributed the highest effect on the slurry slump. Slurry mass concentration is a dominant influential factor in slurry slump, which verifies the reliability of range analysis derived from the orthogonal experiment.
- The filling proportion with satisfactory slurry fluidity is optimized by multi-response robust optimization for Carlin-type gold deposits with ultra-fine tailings. The validation test shows that the cemented filling material proportion is optimal with 68.36% slurry mass concentration, 36.72% waste rock content and 1:3 cement-sand ratio. With this filling proportion, the 7-day and 28-day backfill strengths were 1.94 MPa and 2.56 MPa, respectively, and the slurry slump was 27.5 cm.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Particle Size/mm | wt/% | Particle Size/mm | wt/% | Particle Size/mm | wt/% |
---|---|---|---|---|---|
−5 | 2.23 | 20–40 | 12.24 | 150–200 | 21.96 |
5–10 | 3.06 | 40–80 | 14.53 | 200–300 | 25.34 |
10–20 | 7.44 | 80–150 | 2.15 | +300 | 11.03 |
Component | Au | Fe | Cao | MgO | Al2O3 | SiO2 | S | K | Mn | Si | Loss on Ignition |
---|---|---|---|---|---|---|---|---|---|---|---|
Content/% | 0.00012 | 5.54 | 12.37 | 6.88 | 14.45 | 37.22 | 2.98 | 4.99 | 5.23 | 9.34 | 0.99988 |
Slurry Mass Concentration A (%) | Waste Rock Content B (%) | Cement-Sand Ratio C |
---|---|---|
64 | 25 | 1:3 |
66 | 30 | 1:4 |
68 | 35 | 1:6 |
70 | 40 | 1:8 |
72 | 45 | 1:10 |
Run | Slurry Mass Concentration (%) | Waste Rock Content (%) | Cement-Sand Ratio | Run | Slurry Mass Concentration (%) | Waste Rock Content (%) | Cement-Sand Ratio |
---|---|---|---|---|---|---|---|
1 | 64 | 25 | 1:3 | 14 | 68 | 40 | 1:3 |
2 | 64 | 30 | 1:4 | 15 | 68 | 45 | 1:4 |
3 | 64 | 35 | 1:6 | 16 | 70 | 25 | 1:8 |
4 | 64 | 40 | 1:8 | 17 | 70 | 30 | 1:10 |
5 | 64 | 45 | 1:10 | 18 | 70 | 35 | 1:3 |
6 | 66 | 25 | 1:4 | 19 | 70 | 40 | 1:4 |
7 | 66 | 30 | 1:6 | 20 | 70 | 45 | 1:6 |
8 | 66 | 35 | 1:8 | 21 | 72 | 25 | 1:10 |
9 | 66 | 40 | 1:10 | 22 | 72 | 30 | 1:3 |
10 | 66 | 45 | 1:3 | 23 | 72 | 35 | 1:4 |
11 | 68 | 25 | 1:6 | 24 | 72 | 40 | 1:6 |
12 | 68 | 30 | 1:8 | 25 | 72 | 45 | 1:8 |
Influential Factor | Coding Level | ||
---|---|---|---|
−1 | 0 | 1 | |
Slurry mass concentration (%) | 64 | 68 | 72 |
Waste rock content (%) | 25 | 35 | 45 |
Cement-sand ratio | 1:3 | 1:6 | 1:10 |
Run | Coded Variables | Original Variables | ||||
---|---|---|---|---|---|---|
Slurry Mass Concentration (%) | Waste Rock Content (%) | Cement-Sand Ratio | Slurry Mass Concentration (%) | Waste Rock Content (%) | Cement-Sand Ratio | |
1 | 0 | 0 | 0 | 68 | 35 | 1:6 |
2 | 1 | −1 | 0 | 72 | 25 | 1:6 |
3 | 0 | 1 | −1 | 68 | 45 | 1:3 |
4 | 0 | 0 | 0 | 68 | 35 | 1:6 |
5 | 1 | 1 | 0 | 72 | 45 | 1:6 |
6 | 0 | 1 | 1 | 68 | 45 | 1:10 |
7 | 1 | 0 | 1 | 72 | 35 | 1:10 |
8 | −1 | 1 | 0 | 64 | 45 | 1:6 |
9 | −1 | −1 | 0 | 64 | 25 | 1:6 |
10 | 0 | 0 | 0 | 68 | 35 | 1:6 |
11 | 0 | −1 | 1 | 68 | 25 | 1:10 |
12 | 0 | 0 | 0 | 68 | 35 | 1:6 |
13 | 1 | 0 | −1 | 72 | 35 | 1:3 |
14 | −1 | 0 | 1 | 64 | 35 | 1:10 |
15 | 0 | −1 | −1 | 68 | 25 | 1:3 |
16 | 0 | 0 | 0 | 68 | 35 | 1:6 |
17 | −1 | 0 | −1 | 64 | 25 | 1:3 |
Level of Factors | The Influence of Single Factor on 7-Day Strength Range | The Influence of Single Factor on 28-Day Strength Range | The Influence of Single Factor on Slump Range | ||||||
---|---|---|---|---|---|---|---|---|---|
Slurry Mass Concentration Means (%) | Waste Rock Content Means (%) | Cement-Sand Ratio | Slurry Mass Concentration Means (%) | Waste Rock Content Means (%) | Cement-Sand Ratio | Slurry Mass Concentration Means (%) | Waste Rock Content Means (%) | Cement-Sand Ratio | |
1 | 0.671 | 0.948 | 1.958 | 0.816 | 1.048 | 2.613 | 27.26 | 23.96 | 24.20 |
2 | 0.826 | 1.004 | 1.291 | 1.043 | 1.231 | 1.564 | 26.40 | 24.80 | 25.76 |
3 | 0.928 | 1.093 | 0.799 | 1.176 | 1.351 | 0.954 | 26.24 | 24.80 | 25.38 |
4 | 1.188 | 1.061 | 0.535 | 1.343 | 1.347 | 0.593 | 23.80 | 25.30 | 24.52 |
5 | 1.485 | 0.994 | 0.516 | 1.857 | 1.258 | 0.511 | 20.90 | 25.74 | 24.74 |
Range | 0.814 | 0.145 | 1.442 | 1.041 | 0.303 | 2.102 | 6.36 | 1.78 | 1.56 |
Number | Slurry Mass Concentration (%) | Waste Rock Content (%) | Cement-Sand Ratio | 7-Day Strength (MPa) | 28-Day Strength (MPa) | Slump (cm) |
---|---|---|---|---|---|---|
1 | 0 | 0 | 0 | 0.732 | 0.633 | 28.5 |
2 | 1 | −1 | 0 | 0.904 | 0.919 | 19.2 |
3 | 0 | 1 | −1 | 1.897 | 2.829 | 24.7 |
4 | 0 | 0 | 0 | 0.744 | 0.655 | 28.4 |
5 | 1 | 1 | 0 | 1.119 | 1.515 | 20.6 |
6 | 0 | 1 | 1 | 0.337 | 0.238 | 27.5 |
7 | 1 | 0 | 1 | 0.813 | 0.792 | 22.6 |
8 | −1 | 1 | 0 | 0.567 | 0.550 | 29.1 |
9 | −1 | −1 | 0 | 0.405 | 0.962 | 22.1 |
10 | 0 | 0 | 0 | 0.703 | 0.628 | 28.4 |
11 | 0 | −1 | 1 | 0.387 | 0.656 | 23.2 |
12 | 0 | 0 | 0 | 0.714 | 0.632 | 28.2 |
13 | 1 | 0 | −1 | 2.585 | 3.695 | 19.6 |
14 | −1 | 0 | 1 | 0.244 | 0.641 | 25.4 |
15 | 0 | −1 | −1 | 1.830 | 2.127 | 26.4 |
16 | 0 | 0 | 0 | 0.689 | 0.613 | 28.8 |
17 | −1 | 0 | −1 | 1.475 | 1.801 | 28.9 |
Source of Variation | Sum of Squares | Mean Square | F Value | p Value | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
y1 | y2 | y3 | y1 | y2 | y3 | y1 | y2 | y3 | y1 | y2 | y3 | |
Model | 6.540 | 14.021 | 203.702 | 0.727 | 1.558 | 22.634 | 129.812 | 324.084 | 88.022 | 0.000 | 0.000 | 0.000 |
x1 | 1.034 | 1.617 | 87.745 | 1.034 | 1.617 | 87.745 | 184.773 | 336.457 | 341.233 | 0.000 | 0.000 | 0.000 |
x2 | 0.019 | 0.097 | 7.677 | 0.019 | 0.097 | 7.677 | 3.465 | 20.123 | 29.864 | 0.105 | 0.003 | 0.001 |
x3 | 4.509 | 8.252 | 0.451 | 4.509 | 8.252 | 0.451 | 805.483 | 1716.683 | 1.751 | 0.000 | 0.000 | 0.227 |
x12 | 0.042 | 0.410 | 48.459 | 0.042 | 0.410 | 48.459 | 7.447 | 85.282 | 188.453 | 0.029 | 0.000 | 0.000 |
x22 | 0.019 | 0.008 | 22.614 | 0.019 | 0.008 | 22.614 | 3.383 | 1.575 | 87.946 | 0.108 | 0.251 | 0.000 |
x32 | 0.077 | 0.479 | 2.422 | 0.077 | 0.479 | 2.422 | 13.825 | 99.628 | 9.426 | 0.007 | 0.000 | 0.018 |
x1x2 | 0.001 | 0.254 | 7.840 | 0.001 | 0.254 | 7.840 | 0.132 | 52.849 | 30.494 | 0.734 | 0.000 | 0.001 |
x1x3 | 0.105 | 0.901 | 14.162 | 0.105 | 0.901 | 14.162 | 18.663 | 187.425 | 55.073 | 0.003 | 0.000 | 0.000 |
x2x3 | 0.000 | 0.298 | 12.010 | 0.000 | 0.298 | 12.010 | 0.073 | 62.073 | 46.706 | 0.806 | 0.000 | 0.000 |
7-Day Strength (MPa) | 28-Day Strength (MPa) | Slump (cm) | |||
---|---|---|---|---|---|
calculated value | experimental value | calculated value | experimental value | calculated value | experimental value |
1.988 ± 0.05 | 1.940 | 2.592 ± 0.05 | 2.555 | 27.3 ± 0.5 | 26.9 |
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Huang, M.; Cai, S.; Chen, L.; Tang, S. Multi-Response Robust Parameter Optimization of Cemented Backfill Proportion with Ultra-Fine Tailings. Materials 2022, 15, 6902. https://doi.org/10.3390/ma15196902
Huang M, Cai S, Chen L, Tang S. Multi-Response Robust Parameter Optimization of Cemented Backfill Proportion with Ultra-Fine Tailings. Materials. 2022; 15(19):6902. https://doi.org/10.3390/ma15196902
Chicago/Turabian StyleHuang, Mingqing, Sijie Cai, Lin Chen, and Shaohui Tang. 2022. "Multi-Response Robust Parameter Optimization of Cemented Backfill Proportion with Ultra-Fine Tailings" Materials 15, no. 19: 6902. https://doi.org/10.3390/ma15196902