基于响应面法的复合充填料浆配比优化及微观结构影响机制

刘树龙; 王发刚; 李公成; 刘国磊; 王劼; 齐兆军

doi:10.13801/j.cnki.fhclxb.20201013.001

基于响应面法的复合充填料浆配比优化及微观结构影响机制

doi: 10.13801/j.cnki.fhclxb.20201013.001

1.
山东理工大学　材料科学与工程学院，淄博 255049
2.
山东理工大学　资源与环境工程学院，淄博 255049
3.
山东黄金矿业科技有限公司充填工程实验室分公司，莱州 261400

基金项目: 国家自然科学基金青年项目 (51904178)；国家重点研发计划政府间国际科技创新合作重点专项“地下金属矿规模化绿色开采关键技术合作研究” (2018YFE0123000)；山东省自然科学基金博士基金(ZR2018BEE009)

详细信息

通讯作者:
王发刚，博士，教授，博士生导师，研究方向为矿山充填胶凝材料及化学功能材料　E-mail：a_gang@sdut.edu.cn

中图分类号: TD853
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出版历程
- 收稿日期: 2020-08-20
- 录用日期: 2020-09-23
- 网络出版日期: 2020-10-13
- 刊出日期: 2021-08-15

Optimization of mixture ratio and microstructure influence mechanism of composite filling slurry based on response surface method

1.
11School of Materials Science and Engineering, Shandong University of Technology, Zibo 255049, China
2.
College of Resources and Environmental Engineering, Shandong University of Technology, Zibo 255049, China
3.
Shandong Gold Mining Technology CO. LTD., Filling Engineering Laboratory Branch, Laizhou 261400, China

摘要

摘要: 为探明因素间交互作用对充填体强度性能的影响机制及揭示胶凝材料水化产物作用机制，以水泥、石灰、石膏添加量为自变量影响因子，胶结体抗压强度为响应目标值，采用Box-Behnken响应面法(RSM)设计试验，建立二次多项式回归模型，结合Numencial功能优化模型自变量参数。最后，利用XRD、SEM、EDS分析手段，探讨净浆试样水化产物组成及微观结构形貌。研究结果表明∶方差分析及模型响应曲面共同诠释了水泥和石灰添加量的交互作用是影响充填体强度性能的关键性因素。对复合充填料浆配合比寻优可得，在水泥∶石灰∶石膏∶矿渣∶甲酸钙=30∶15∶1∶50∶4最优条件下，胶结体3天和7天抗压强度为1.19 MPa和2.17 MPa，模型验证试验相对误差为3.25%和0.93%，表明模型精确度高，可靠性强。复合胶凝体系水化产物主要为钙矾石(AFt)和C-S-H凝胶，随着龄期的延长，AFt和C-S-H凝胶交错生长，紧密搭接，形成致密的三维空间网络结构支撑体系，是胶结充填体具备强度性能的主要来源。
- 响应面法 /
- 交互作用 /
- 回归模型 /
- 抗压强度 /
- 最优配比 /
- 微观结构
Abstract: To explore how the interaction among factors influences the strength of filling body, and reveal the action mechanism of hydration products from cement materials, a test was designed by Box-Behnken response surface methodology (RSM) for establishing a quadratic polynomial regression model in combination with independent variable parameters of numencial function optimization model. In the design, the added quantities of cement, lime and gypsum were taken as independent variable influence factors, and the compressive strength of cement body as the response target values. Finally, XRD, SEM and EDS analysis methods were utilized to discuss the composition and microstructure morphology of the hydration products from paste samples. The results show that the ANOVA and the response surface of the model jointly explain that the interaction between cement and lime quantities added is the critical factor influencing the strength of filling body. After optimizing the mixture ratio of the composite filling slurry, when the ratio of cement∶lime∶gypsum∶slag∶calcium formate is optimal as 30∶15∶1∶50∶4, the 3 days and 7 days compressive strength values of the cement body are 1.19 MPa and 2.17 MPa, respectively. The relative errors of the model validation tests are 3.25% and 0.93%, which indicates that the model is precise and reliable. The main hydration products of the composite cementitious system are AFt and C-S-H gels, which stagger and overlap closely with age, thus forming a dense 3D spatial network structure support system as the main source of strength for the cemented filling body.
- response surface method /
- interaction /
- regression model /
- compressive strength /
- optimal ratio /
- microstructure

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图 1 尾砂的XRD图谱

Figure 1. XRD pattern of tailings

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图 2 尾砂粒径分布曲线

Figure 2. Distribution curves of tailings particle size

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图 3 胶结剂微观结构形貌

Figure 3. Microstructure and morphologies of cement

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图 4 甲酸钙的XRD图谱

Figure 4. XRD pattern of calcium formate

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图 5 胶结体抗压强度试验值与预测值对比

Figure 5. Comparison of the experimental and predicted values of cement compressive strength

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图 6 胶结体抗压强度的三维响应曲面图

Figure 6. Three-dimensional response curve of compressive strength of cement

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图 7 净浆试样不同龄期水化产物的物相组成

Figure 7. Phase composition of hydration products of pure pulp samples at different ages

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图 8 不同龄期净浆试样水化产物SEM微观形貌及EDS图谱

Figure 8. SEM micro-morphology and EDS spectra of hydration products of pure pulp samples at different ages

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表 1 尾砂主要化学成分组成

Table 1. Main chemical composition of tailings

Test No.	Chemical component	Mass fraction/wt%
1	SiO₂	62.60
2	Al₂O₃	15.20
3	CaO	2.31
4	K₂O	5.86
5	Na₂O	3.10
6	Fe₂O₃	1.16
7	TiO₂	0.22
8	MgO	0.90
9	SO₃	0.40
10	P₂O₅	0.09
11	MnO	0.03
12	Others	8.13

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表 2 胶结剂主要化学成分组成

Table 2. Main chemical composition of cement

Chemical component	Mass fraction/wt%
Chemical component	Slag	Cement	Lime	Gypsum
CaO	43.80	45.80	95.50	46.40
Al₂O₃	16.50	15.50	0.43	0.17
SiO₂	26.90	25.50	1.75	1.26
Na₂O	0.39	0.72	0.10	0.09
MgO	7.10	3.94	1.28	3.24
Fe₂O₃	0.58	2.88	0.35	0.18
SO₃	2.87	3.56	0.30	48.10
Others	1.86	2.10	0.29	0.56

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表 3 响应面因素设计与水平编码

Table 3. Response surface factor design and horizontal coding

Level	A/wt%	B/wt%	C/wt%
−1	10	5	1
0	20	10	2
1	30	15	3
Notes：A—Cement; B—Lime; C—Gypsum.

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表 4 复合充填料浆响应面试验设计与测试结果

Table 4. Response surface test design and test results of composite filling slurry

Test No.	Coded value			R_3d/MPa		R_7d/MPa
Test No.	A/wt%	B/wt%	C/wt%	Actual value	Predicted value	Actual value	Predicted value
1	0	0	0	0.68	0.68	1.26	1.22
2	0	0	0	0.68	0.68	1.27	1.22
3	0	−1	−1	0.58	0.58	1.11	1.11
4	0	1	1	0.82	0.82	1.33	1.34
5	−1	−1	0	0.28	0.30	0.45	0.51
6	0	0	0	0.68	0.68	1.26	1.22
7	1	−1	0	0.99	0.98	1.63	1.59
8	1	0	−1	1.05	1.06	1.84	1.93
9	0	0	0	0.69	0.68	1.27	1.22
10	0	0	0	0.68	0.68	1.25	1.22
11	1	0	1	1.12	1.14	1.61	1.73
12	−1	0	−1	0.34	0.32	0.65	0.64
13	1	1	0	1.26	1.24	2.15	2.07
14	0	−1	1	0.63	0.62	1.02	0.99
15	0	1	−1	0.74	0.75	1.42	1.46
16	−1	1	0	0.41	0.42	0.71	0.73
17	−1	0	1	0.37	0.36	0.58	0.60
Notes：R_3d—Uniaxial compressive strength of 3rd day; R_7d—Uniaxial compressive strength of 7th day.

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表 5 响应面回归模型方差分析

Table 5. Analysis of variance of response surface regression model

Curing age/day	Source	Sum of square	DF	Mean square	F-value	P-value	Significance
3	Model	1.23	9	0.14	545.22	<0.0001	***
	A	1.14	1	1.14	4 547.21	<0.0001	***
	B	0.070	1	0.070	280.45	<0.0001	***
	C	6.613×10⁻³	1	6.613×10⁻³	26.37	0.0013	**
	AB	4.900×10⁻³	1	4.900×10⁻³	19.54	0.0031	**
	AC	4.000×10⁻⁴	1	4.000×10⁻⁴	1.60	0.2470	*
	BC	2.250×10⁻⁴	1	2.250×10⁻⁴	0.90	0.3750	*
	A²	6.821×10⁻³	1	6.821×10⁻³	27.21	0.0012	**
	B²	6.845×10⁻⁴	1	6.845×10⁻⁴	2.73	0.1425	*
	C²	2.132×10⁻⁵	1	2.132×10⁻⁵	0.085	0.7791	*
	Residual	1.755×10⁻³	7	2.507×10⁻⁴	—	—	—
	Lack of fit	1.675×10⁻³	3	5.583×10⁻⁴	27.92	0.0038	**
	Pure error	8.000×10⁻⁵	4	2.000×10⁻⁵	—	—	—
	Cor total	1.23	16	—	—	—	—
R²=0.9986		R_Adj²=0.9967		R_Pred²=0.9781		C_V=2.24%
	Source	Sum of square	DF	Mean square	F-value	P-value	Significance
7	Model	3.23	6	0.54	120.23	<0.0001	***
	A	2.93	1	2.93	654.91	<0.0001	***
	B	0.25	1	0.25	54.80	<0.0001	***
	C	0.029	1	0.029	6.44	0.0295	**
	AB	0.017	1	0.017	3.78	0.0805	*
	AC	6.400×10⁻³	1	6.4×10⁻³	1.43	0.2591	*
	BC	0.000	1	0.000	0.000	1.000	*
	Residual	0.045	10	4.471×10⁻³	—	—	—
	Lack of fit	0.044	6	7.405×10⁻³	105.79	0.0002	**
	Pure error	2.800×10⁻⁴	4	7.000×10⁻⁵	—	—	—
	Cor total	3.27	16	—	—	—	—
R²=0.9863		R_Adj²=0.9781		R_Pred²=0.9389		C_V=5.46%
Notes：DF—Degree freedom; F-value—Ratio of the mean square to the residual term; P-value—Influence degree value of each factor; *—Significant in [-∞,0.0001]; —Significant in [0.0001,0.05]; *—Significant in [0.05,+∞]; R²—Complex correlation coefficient; R_Adj²—Correction correlation coefficient; R_Pred²—Predictive correlation coefficient; C_V—Coefficient of variation.

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表 6 胶结体响应面预测模型验证试验结果

Table 6. Response surface prediction model verification test results of cement

Curing age	3 days	7 days
Predicted value/MPa	1.19	2.17
Actual value/MPa	1.25	2.17
	1.23	2.16
	1.20	2.14
	1.26	2.15
	1.21	2.14
Average value/MPa	1.23	2.15
Error/%	3.25	0.93

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