The Optimization of Mix Proportions for Cement Paste Backfill Materials via Box–Behnken Experimental Method
- 66 Downloads
Abstract
Cemented paste backfill (CPB) technology has been applied quite popular around the world. Determining a reliable filling material mix proportions is an important aspect of mine backfilling. To produce effective CPB materials at copper mines technologically and economically, Box–Behnken design experimental program (four factors and three levels) was carried out to test the optimal mix proportions with unclassified tailings. Results of the test indicated that slump decreased first and then increased with the increase in the pumping agent content. However, the slump decreased with the mass concentration, cement content and tailing/rock ratio. And 28-day uniaxial compressive strength (UCS) was positively correlated with rock content and mass concentration. The sensitive degrees of each variable to the slump and UCS were determined, and the influence of law and mechanism of each factor on the response value was analyzed. Relationships of paste properties and influential factors can be demonstrated with regression analysis. Additionally, the optimal mix proportion for cement paste backfill was obtained with 76.75% mass concentration, 3.35 tailing/rock ratio, 0.1 cement/(tailing + rock) ratio and 1.24% pumping agent addition. The slump and UCS of the optimal mixture were 24.1 cm and 1.59 MPa, respectively. The experimental results showed a feasible way to produce the industry standard backfilling materials.
Keywords
Unclassified tailings Cement paste backfill Mix proportion Box–Behnken design Experimental optimizationIntroduction
In order to meet the needs of sustainable economic development, the development of mineral resources is growing. With the depletion of shallow surface resources and the growing demand for mineral resources in social development, deep well mining will be the future direction of mining [1, 2]. Due to the characteristics of deep mining high stress, high ground pressure and high ground temperature, coupled with the sustainable development trend of building green mines and mining, the backfilling mining method has become the preferred method for deep mining. CPB technology is favored by mining enterprises because of its non-stratification, non-segregation and non-precipitation characteristics [3]. CPB not only reduces the consumption of cement, but also effectively supports the roof, reduces drainage and makes the tailings produced by the mine fully utilized [4, 5]. This not only controls the cost of filling the goaf significantly, but also improves the environmental pollution problem and promotes the sustainable development of the mine [6].
Paste is normally produced by coarse particles, fine particles and binders with specific mix proportions, and transported to underground stopes through reticulated pipelines. Due to the large amount of waste rock on the surface of the mine, the addition of waste rock can increase the strength of the filling body. The amount of cement determines the cost of mine filling, and using a small cement/(tailing + rock) ratio as much as possible can save costs. When the pressure of the filling pipe of the mine is large, the pumping agent can be appropriately added to reduce the resistance of the pipe to protect the pipeline and the pump. Therefore, the mass concentration, tailing/rock ratio (T/R), cement/(tailing + rock) ratio [C/(T + R)] and pumping agent addition were selected as the research object. Generally, the targeted physical and chemical properties of CPB are apparently affected by many parameters such as mobility, yield stress and UCS. However, UCS is an important criterion for determining the filling effect of mine goaf and whether the filling body can support the surrounding rock well. The slump determines whether the pipeline can safely and stably transport the paste slurry to the gob. Therefore, mix proportions of different materials are critical to obtain high-quality CPB with required industrial parameters.
Response surface methodology is an analysis method that analyzes the influence of multiple factors on the target variable (response value) based on the experimental data [7]. It can use the multivariate nonlinear regression method to establish the mathematical model between the response value and each influencing factor, and then seek the optimal experimental conditions [8]. Box–Behnken is a response surface design method, especially for the study of factors ranging from 3 to 7. Multivariate quadratic equations can be used to fit the functional relationship between multiple factors and response values, analyze the response value and the nonlinear relationship between the various factors [9]. The paper used this method based on a certain number of experiments; the effects of the mass concentration, tailing/rock ratio, cement/(tailing + rock) ratio, pumping agent addition and their interaction on the slump and UCS were comprehensively analyzed to obtain the optimal experimental conditions. Based on the experimental data, range analysis was introduced to understand the sensitive degrees of each variable to targeted properties, and regression analysis was used to quantitatively demonstrate the relationships between independent variables and dependent variables. The work showed that the combination of Box–Behnken design, range analysis and regression analysis was a feasible way to produce the satisfied cemented paste backfilling materials.
Materials and Methods
Tailings
Rocks
The rock samples were taken from the surface waste rock near the mine and were milled to − 10 mm for transport to the laboratory. The density is 2.667 t/m^{3}, the loose bulk density of waste rock is 1.524 t/m^{3}, the dense bulk density is 1.863 t/m^{3}, and the porosity is 22.6%–31.6%. The X-ray fluorescence test showed that the composition of rocks was similar to the tailings. The \( C_{\text{U}} \) and \( C_{\text{C}} \) values are 17.05 and 1.47, respectively. Combined with the granular distribution of rock as shown in Fig. 1, it could be seen that the rocks size distribution range was wide and the rock grade was better.
Cements
The 42.5R Portland cement was used. The cement has a specific surface area of 415 m^{2}/kg, density of 3.03 t/m^{3} and dense bulk density of 1.424 t/m^{3}. The granular distribution is shown in Fig. 1.
Pumping Agent
Through the paste additive test, the JK-5-type pumping agent was selected as an admixture for backfilling, polycarboxylic acid type and powder form. The amount of pumping agent added is the weight percent of the cement.
Experimental Approach
Box–Behnken design experimental factors level and codes
Factor | Unit | Level (− 1) | Level (+ 1) |
---|---|---|---|
x_{1}—mass concentration | wt% | 76 | 78 |
x_{2}—T/R | – | 2 | 4 |
x_{3}—C/(T + R) | – | 0.05 | 0.17 |
x_{4}—pumping agent addition | % | 1 | 2.5 |
Box–Behnken design experiment result
Mixture | Mass concentration (wt%) | T/R | C/(T + R) | Pumping agent addition (%) | Slump (cm) | UCS (MPa) |
---|---|---|---|---|---|---|
1 | 76 | 3 | 0.17 | 1.75 | 25.6 | 4.75 |
2 | 76 | 4 | 0.11 | 1.75 | 27.6 | 1.41 |
3 | 77 | 4 | 0.11 | 1 | 22.3 | 1.63 |
4 | 76 | 3 | 0.05 | 1.75 | 26.8 | 0.29 |
5 | 76 | 2 | 0.11 | 1.75 | 25.4 | 2.36 |
6 | 77 | 3 | 0.11 | 1.75 | 23.8 | 2.01 |
7 | 78 | 2 | 0.11 | 1.75 | 27.6 | 2.42 |
8 | 77 | 3 | 0.17 | 2.5 | 24.9 | 5.08 |
9 | 77 | 2 | 0.11 | 1 | 27.6 | 2.19 |
10 | 77 | 3 | 0.05 | 1 | 25.2 | 0.35 |
11 | 77 | 3 | 0.11 | 1.75 | 24.2 | 1.91 |
12 | 78 | 3 | 0.11 | 2.5 | 22.6 | 2.33 |
13 | 78 | 3 | 0.17 | 1.75 | 20.4 | 5.19 |
14 | 77 | 3 | 0.17 | 1 | 24.9 | 4.51 |
15 | 77 | 2 | 0.11 | 2.5 | 28.3 | 2.22 |
16 | 77 | 4 | 0.05 | 1.75 | 21.9 | 0.76 |
17 | 78 | 4 | 0.11 | 1.75 | 14.5 | 2.36 |
18 | 77 | 4 | 0.17 | 1.75 | 20.7 | 4.78 |
19 | 76 | 3 | 0.11 | 1 | 27.5 | 1.56 |
20 | 78 | 3 | 0.05 | 1.75 | 21.7 | 0.98 |
21 | 77 | 3 | 0.11 | 1.75 | 24 | 1.8 |
22 | 77 | 2 | 0.05 | 1.75 | 27.2 | 0.54 |
23 | 77 | 3 | 0.05 | 2.5 | 26.7 | 0.59 |
24 | 77 | 3 | 0.11 | 1.75 | 24 | 2.23 |
25 | 77 | 4 | 0.11 | 2.5 | 23 | 1.87 |
26 | 77 | 3 | 0.11 | 1.75 | 24.1 | 1.99 |
27 | 78 | 3 | 0.11 | 1 | 22 | 2.24 |
28 | 77 | 2 | 0.17 | 1.75 | 26.1 | 5.23 |
29 | 76 | 3 | 0.11 | 2.5 | 28.2 | 1.66 |
Paste Properties Test
Slurry was prepared according to the designed mix proportions of tailings, rocks, cement, pumping agent and water. The slump was tested following the China national standard for test method of performance on ordinary fresh concrete (GB/T 50080-2002) [10]. The UCS tests were carried out according to the China national standard for test method of mechanical properties on ordinary concrete (GB/T 50081-2002) [11].
Results and Discussion
Experimental Results of Paste Mix Proportions
Table 2.
Data Processing and Analysis
Regression Analysis
Variance and Significance Analysis
Box–Behnken design regression model analysis of variance
Response | Source | Sum of squares | df | Mean square | F value | P value |
---|---|---|---|---|---|---|
Model | 252.42 | 14 | 18.03 | 879.01 | < 0.0001 | |
x _{1} | 86.94 | 1 | 86.94 | 4238.55 | < 0.0001 | |
x _{2} | 86.40 | 1 | 86.40 | 4212.35 | < 0.0001 | |
x _{3} | 3.97 | 1 | 3.97 | 193.42 | < 0.0001 | |
x _{4} | 1.47 | 1 | 1.47 | 71.67 | < 0.0001 | |
x _{1} x _{2} | 58.5225 | 1 | 58.5225 | 2853.099 | < 0.0001 | |
Slump | x _{1} x _{3} | 0.0025 | 1 | 0.0025 | 0.12188 | 0.7322 |
x _{1} x _{4} | 0.0025 | 1 | 0.0025 | 0.12188 | 0.7322 | |
x _{2} x _{3} | 0.0025 | 1 | 0.0025 | 0.12188 | 0.7322 | |
x _{2} x _{4} | 2.84E−14 | 1 | 2.84E−14 | 1.39E−12 | 1.0000 | |
x _{3} x _{4} | 0.5625 | 1 | 0.5625 | 27.4231 | 0.0001 | |
Residual | 0.29 | 14 | 0.021 | – | – | |
Lack of fit | 0.20 | 10 | 0.020 | 0.91 | 0.5936 | |
Pure error | 0.088 | 4 | 0.022 | – | – | |
Cor. total | 252.71 | 28 | – | – | – | |
UCS | Model | 62.42 | 14 | 4.46 | 237.49 | < 0.0001 |
x _{1} | 1.02 | 1 | 1.02 | 54.06 | < 0.0001 | |
x _{2} | 0.39 | 1 | 0.39 | 20.52 | 0.0005 | |
x _{3} | 56.46 | 1 | 56.46 | 3007.41 | < 0.0001 | |
x _{4} | 0.13 | 1 | 0.13 | 7.16 | 0.0181 | |
x _{1} x _{2} | 0.198025 | 1 | 0.198025 | 10.5474 | 0.0058 | |
x _{1} x _{3} | 0.015625 | 1 | 0.015625 | 0.832234 | 0.3771 | |
x _{1} x _{4} | 2.5E−05 | 1 | 2.5E−05 | 0.001332 | 0.9714 | |
x _{2} x _{3} | 0.112225 | 1 | 0.112225 | 5.977439 | 0.0283 | |
x _{2} x _{4} | 0.011025 | 1 | 0.011025 | 0.587224 | 0.4562 | |
x _{3} x _{4} | 0.027225 | 1 | 0.027225 | 1.450085 | 0.2485 | |
Residual | 0.26 | 14 | 0.019 | – | – | |
Lack of fit | 0.16 | 10 | 0.016 | 0.65 | 0.7381 | |
Pure error | 0.1 | 4 | 0.025 | – | – | |
Cor. total | 62.69 | 28 | – | – | – |
Both regression equations reached a very significant level (P < 0.01). The lack of fit of Eq. (2) was 0.5936 > 0.05, which was not significant, indicating that the equation was consistent with the experimental data and the stability was high. Model correlation coefficient R^{2} = 0.9989, and correction coefficient R _{adj} ^{2} = 0.9977. The lack of fit of Eq. (3) was 0.7381 > 0.05, which was not significant, R^{2} = 0.9958, R _{adj} ^{2} = 0.991. It was indicated that the predicted value of the slump and UCS of the Box–Behnken design experiment had a good fitting degree to the actual value obtained by the experiment. The equation had high authenticity and high confidence. Therefore, the equation can be used to analyze and predict the slump value and UCS in the mix proportion of CPB.
Analysis of the Significance of Single-Factor Influence
Analysis of the Significance of Factor Interaction
For the fitting results of the response surface, the contour shape and the three-dimensional surface can reflect the strength of the interaction between the factors. Some researches have shown that if the color changes faster in the 3D surface region, the steeper the surface, the more sensitive the response value is to the change in the two factors [12]. Some analysts believe that the contour is elliptical, indicating that the interaction between the two influencing factors is obvious; the contour is circular, and the interaction between the two influencing factors is not significant [13].
Analysis of the Effect of the Interaction of Experimental Factors on the Slump Value
- 1.
Analysis of the interaction effect of factor x_{1}x_{2}
- 2.
Analysis of the interaction effect of factor x_{3}x_{4}
On the other hand, the cement particles are small and have a large specific surface area, which could absorb more water than the aggregate. As the cement content increased, the fine particle mass fraction increased, the contact and friction between the fine aggregates increased, the ability to plastically deform of the slurry was reduced, and the plastic viscosity was increased. So, the macroscopic performance of the slump was reduced, and the rheology was deteriorated.
Analysis of the Effect of Interaction of Experimental Factors on UCS
- (1)
Effect of mass concentration on UCS
The general mass concentration of the filling slurry was 70–80%. The particles were not freely settled, but interference settlement, which would slow down the difference of sedimentation, was caused by different particle sizes. However, the general trend did not change, basically it was still the large particles with some of the small particles that sank below, above were the smaller particles of particle size.
- (2)
Effect of T/R on UCS
The UCS of the paste test block increased with the increase in the amount of rock added, but the actual UCS value did not increase much. Under the appropriate grading conditions, the larger particle size aggregate could obtain higher UCS and the best compacting effect also could be obtained, thereby improving the mechanical strength. According to the viewpoint of concrete science, in the combined structure of the cement slurry and the aggregate, the cement slurry is a dispersion medium and the aggregate is a dispersed phase. The aggregate constitutes the skeleton of the CPB, which affects the mechanical strength of the CPB through denseness effect, frame effect, interface effect and mixing effect.
From Fig. 7, when the unclassified tailings were mixed with the rock, the compactness of the aggregate was obviously improved only when the rock content reached 40% or more. In the experiment, in all the mixing ratios, the rock content was only 20% to 33%, although the compactness rose faster, the actual value was not increased much, and the skeleton dense structure was not formed; therefore, the influence on the UCS was small.
Optimization of Paste Mix Proportions
Using the numerical function of optimization in Design Expert software, the slump degree satisfied 20–25 cm and the UCS satisfied 1–2 MPa within the range of influencing factors. The optimal mix proportion for CPB was obtained with 76.75% mass concentration, 3.35 T/R, 0.1 C/(T + R) and 1.24% pumping agent addition. The slump and UCS of the mixture were 24.5 cm and 1.53 MPa, respectively.
The three sets of verification experiments were repeated in parallel under optimized conditions, and the average values of the slump and UCS were 24.1 cm and 1.59 MPa, respectively. The results show that the experimental values of the Box–Behnken design optimization experiment were basically consistent with the predicted values, indicating that the prediction model was effective.
Finally, the optimized mix proportions were applied to the Beishtamu copper mine and achieved a good filling effect, and met the needs of mine production. Box–Behnken design method further realizes the efficient mining of mines and ensures the safety of mining operations and can provide reference for the mining of other similar mines.
Conclusions
- 1.
Experimental factors consist of mass concentration, cement/(tailing + rock) ratio, tailing/rock ratio and pumping agent addition. A Box–Behnken design experiment (four factors and three levels) is carried out. Results of the test indicate that slump decreases first and then increases with the increases in the pumping agent content. However, the slump decreases with the mass concentration, cement content and T/R. UCS is positively correlated with rock content and mass concentration. Furthermore, the range analysis of Box–Behnken design experiments shows that the sensitivity of influential factors to slurry slump is T/R > mass concentration > pumping agent addition > C/(T + R); the sensitivity to UCS is C/(T + R) > mass concentration > T/R > pumping agent addition. The relationships of CPB properties (slump and UCS) and influential factors can be quantitatively demonstrated with equations derived from regression analysis.
- 2.
The causes and mechanisms of the influence of four factors on slump and UCS are analyzed. Firstly, the reasons for the influence of various factors on the slump are explained from the perspective of floc structure, collision friction between particles and free water content. Then, the grain size distribution causes a stable ionic electric double layer to form around the fine particles; the interaction between them and the difference in the flocculation settling velocity form a sedimentary layer distributed according to the particles size, large particles together with some small particles sink below, above are more small particle sizes, which explains the effect of mass concentration on UCS. Finally, from the relationship between the amount of rock and compactness, the experimental data of the Beishtamu copper mine filling tailings ratio do not form a skeleton dense structure, the actual value of UCS increases little.
- 3.
The optimal mix proportion for cement paste backfill with unclassified tailings is obtained with 76.75% mass concentration, 3.35 tailing/rock ratio, 0.1 cement/(tailing + rock) and 1.24% pumping agent addition. The three sets of verification experiments were repeated in parallel under optimized conditions; the average values of the slump and UCS of the mixture are 24.1 cm and 1.59 MPa, respectively.
Notes
Acknowledgements
The authors are thankful to the State Key Laboratory, High-efficient Mining and Safety of Metal Mines, Ministry of Education.
Funding
This research was funded by the National Natural Science Foundation of China, Grant Number (51574013).
References
- 1.H.Z. Jiao, H.J. Wang, A.X. Wu, X.W. Ji, Q.W. Yan, Rule and mechanism of flocculation sedimentation of unclassified tailings. J Univ Sci Technol Beijing 32(6), 702–707 (2010)Google Scholar
- 2.Y.X. Ke, X.M. Wang, Q.L. Zhang, Flocculating sedimentation characteristic of pre-magnetized crude tailings slurry. Chin J Nonferrous Metals 27(2), 392–398 (2017)Google Scholar
- 3.J. Henriquez, P. Simms, Dynamic imaging and modelling of multilayer deposition of gold paste tailings. Miner. Eng. 22(2), 128 (2009)CrossRefGoogle Scholar
- 4.N. Sivakugan, R.M. Rankine, K.J. Rankine, Geotechnical considerations in mine backfilling in Australia. J. Clean. Prod. 14(12–13), 1168 (2006)CrossRefGoogle Scholar
- 5.Z.H. Guo, H.Q. Zhou, L.F. Wu, Numerical simulation for roof and surface subsidence process caused by paste filling. J Min Saf Eng 25(2), 172 (2008)Google Scholar
- 6.L. Liu, Research on Proportion Optimization and Flow Characteristic of Backfill Paste in Mine Sites. Dissertation, Central South University, Changsha (2013)Google Scholar
- 7.Y.X. Zhang, X. Wang, T. Hou, Efficient microwave-assisted production of biofuel ethyl levulinate from corn stover in ethanol medium. J Energy Chem 27(03), 890–897 (2018)CrossRefGoogle Scholar
- 8.S. Kumar, R. Venugopal, Performance analysis of jig for coal cleaning using 3D response surface methodology. Int J Min Sci Technol 27(02), 333–337 (2017)CrossRefGoogle Scholar
- 9.X.Y. Qiu, J.Y. Chen, X.Z. Shi, Deformation prediction and analysis of underground mining during stacking of dry gangue in open-pit based on response surface methodology. J Cent South Univ 25(02), 406–417 (2018)CrossRefGoogle Scholar
- 10.Ministry of Construction of the People’s Republic of China, Standard for Test Method of Performance on Ordinary Fresh Concrete (GB50080-2002) (China Building Industry Press, Beijing, 2003)Google Scholar
- 11.Ministry of Construction of the People’s Republic of China, Standard for Test Method of Mechanical Properties on Ordinary Concrete (GB50081-2002) (China Building Industry Press, Beijing, 2003)Google Scholar
- 12.S.K. Rai, R. Konwarh, A.K. Mukherjee, Purification, characterization and biotechnological application of an alkaline β-keratinase produced by Bacillus subtilis RM-01 in solid-state fermentation using chicken-feather as substrate. Biochem. Eng. J. 45(3), 218–225 (2009)CrossRefGoogle Scholar
- 13.Y.B. Wang, Y.X. Wang, Optimization of cultivation conditions for extracellular polysaccharide fermented by Ustilago maydis using response surface methodology. China Brew 5, 56–60 (2006)Google Scholar
- 14.L. Wang, J.C. Li, J.F. Zhou, Numerical study of flocculation settling of cohesive sediment. Acta Phys Sin 59(05), 3315–3323 (2010)Google Scholar
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.