# The Dosage of Superplasticizer in Cemented Coal Waste Backfill Material Based on Response Surface Methodology

Authors: Qingdong Li; Guorui Feng; Yuxia Guo; Tingye Qi; Xianjie Du; Zehua Wang; Huayun Li
Journal: Advances in Materials Science and Engineering
 (2019)

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## Abstract

Cemented coal waste backfill material (CCWBM) is developed for backfilling the goaf in coal mines. As fresh CCWBM slurry is generally transported into underground openings through a pipeline, the fluidity of fresh slurry becomes one of the most important properties. Adding superplasticizer is considered to improve the flow performance of the slurry without alerting the mechanical performance of filling body. The dosage of superplasticizer (SP) is related to filling cost, thus response surface methodology (RSM) is adopted to study the influence of material composition on SP when target slump is 250 mm. The effects of fly ash content, fine gangue ratio, and mass concentration on SP are analyzed using the software of Design-Expert and central composite design (CCD), and models are established for SP. Results show that the SP model coincides greatly with the test results and can be applied to analyze and predict SP in CCWBM. Mass concentration, fly ash content, and fine gangue ratio influence SP from high to low. The interaction of fine gangue ratio and mass concentration between SP is the most significant. The fact that the improved aggregate space model can be applied to analyze the fluidity of CCWBM is proved too. The research results provide guidance for the design and preparation of CCWBM with favourable performance and low cost in practical production.


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## Body

## 1. Introduction

In China, underground coal mines produce about 95% of total coal [1]. Underground coal mining indeed contributes a large amount of coal, but it also creates a tremendous amount of mined-out void and discharges a great deal of solid waste [2, 3]. Most of the waste is coal gangue, and it is reported that approximately 4.5 billion tons of coal gangue is stocked in China at present [4]. The waste is simply disposed aboveground and stockpiled in waste dumps, which causes serious environmental problems. On one hand, the waste dumps occupy much land and the poisonous substance contained in the waste contaminates soil and under water [1, 5]. On the other hand, the spontaneous combustion of the waste leads to air pollution or even personal injury. Meanwhile, underground void results in land surface subsidence [6, 7]. Cemented coal waste backfill material (CCWBM), which is an engineered mixture of crushed coal gangue, fly ash, cement, and water, is developed for mine backfilling [8–11]. All the problems aforesaid can be solved by backfilling CCWBM into the goaf [5, 9, 12, 13].Generally, filling slurry is prepared in a filling plant and then transported to underground openings, thereby necessitating the use of sufficient water to gain favourable fluidity [14]. But this could lead to a high water/cement ratio, which will lower the strength and durability of filling body [15, 16]. Considering this challenge, the additive of superplasticizer into CCWBM is considered to reduce mixing water to enhance mechanical properties. Several studies have been conducted on the influences of superplasticizer on the properties of backfill materials. Ercikdi et al. discussed the influences of various superplasticizers, lignosulfonate (EUCO-FILL 30), naphthalene sulfonate (IKSAMENT NS), and polycarboxylate-based superplasticizer (POLYCAR-100), on the properties of CPB [17]. The amount of superplasticizer for lignosulfonate, naphthalene sulfonate, and polycarboxylate was 7%, 6%, and 5.4% (by dry binder mass), respectively, to reach the designed slump (7 inches). The authors reported that superplasticizers reduced water content (∼6.6%), enhanced mechanical properties (20–50%), and improved durability. Simon et al. studied the effects of polycarboxylate-based superplasticizer on flow characteristics and mechanical performance of CPB [18]. It was found that the addition of 4% (by dry binder mass) polycarboxylate-based superplasticizer lowered the yield stress of fresh slurry from 1000 Pa to 3 Pa, but fluidity loss remains to occur over time. In addition, the compressive strength increased from 450 kPa to 1000 kPa. Mangane et al. investigated the mechanical performance and the workability of CPB containing various superplasticizers [14]. The results showed that polycarboxylate had the best performance and achieved the target consistency at lower water content (between 6 and 10%) while still conserving the mechanical strength of CPB. Using polycarboxylate-based superplasticizer could also achieve a reduction in binder content (from 5 to 3%) without alerting the mechanical strength of CPB. Huynh et al. found that naphthalene sulfonate formaldehyde condensate (NSF) and polyphosphate-based superplasticizer affected the rheological properties of CPB with Portland cement by influencing the zeta potential of tailings and cement particles [19]. Moreover, the flow performance of CPB mixed with blended Portland cement slag could be significantly enhanced by adding polycarboxylate-based superplasticizer as reported by Ouattara et al. [20]. Although the above research on CPB has achieved important results, these results cannot be directly applied to CCWBM because CPB is substantially different from CCWBM in material composition [5]. So, it is essential to acquire more information about the dosage of superplasticizer (SP), which relates to filling cost and the influence of superplasticizer on the flow characteristic and mechanical performance of CCWBM.Dong et al. demonstrated that for high density filling slurry, pressure head loss was minimal when the slump of fresh slurry was 250 mm [21]. Therefore, the slump of all mixtures in the present study is set as 250 mm, and the dosage of superplasticizer is adjusted to reach target slump for all mixtures. The variation of superplasticizer dosage is studied when the mix proportion of CCWBM is changed. Fly ash content, fine gangue ratio, and mass concentration are the three key parameters which decide the mix composition of CCWBM, thus this paper studies SP through analyzing the influences of these three factors.Though the method of single variable and orthogonal design is often used to analyze the effects of various factors on targets, test quantity is large and the interaction among various factors cannot be analyzed [22]. Response surface methodology (RSM) is usually adopted to reflect the influence of the factors on the targets and their interaction with three-dimensional image, which is an integration method of mathematics and statistics. Since it came into being in 1951, RSM has been broadly put into use among agriculture, biology, chemistry, and other fields, yet rarely in backfill materials [23, 24]. In accordance with this, RSM is adopted to analyze the effects and their interaction with the three factors aforesaid.In the present study, Design-Expert software is applied to discuss the influences of fly ash content, fine gangue ratio, and mass concentration on SP when target slump is 250 mm. An improved aggregate space model is introduced to explain the variation of SP. The research results provide a reference for subsequent research and practical production of CCWBM.


## 2. Materials and Methods

### 2.1. Raw Materials

The investigated mixtures were systematically proportioned using coal gangue obtained from Xinyang Colliery, a mine in Shanxi Province of China. The samples were mechanically crushed and then categorized into two groups based on particle size, fine gangue aggregate with MSA of 5 mm and coarse gangue aggregate with MSA of 15 mm. The total gangue in each cubic filling slurry was 950 kg. The fineness modulusμ of the fine gangue aggregate was 3.02. A class F fly ash combined with ordinary Portland cement (CEM I 42.5N) (binary system) was used, and the integral dose of binder was 570 kg/m3. The main chemical components and physical properties of coal gangue, cement, and fly ash are summarized in Table 1 [7]. A naphthalene sulphonate-based superplasticizer in powder was incorporated in all mixtures to reach target slump.Table 1
Chemical and physical properties of coal gangue, fly ash, and cement [7].
Coal gangue
Fly ash
Cement
SiO2
28.46
52.42
22.36
Al2O3
16.11
32.48
5.53
Fe2O3
10.86
3.62
3.45
CaO
7.15
3.05
65.08
MgO
3.50
1.01
1.27
TiO2
0.80
1.26
—
Specific gravity (g/cm3)
2.0
2.2
3.1
Specific surface (m2/kg)
499
415
349
Fineness (>45μm) (%)
53.78
42.54
5
Moisture content (%)
8.0
0.56
—
Loss on ignition (%)
—
3.8
2


### 2.2. Test Methods

The required workability of CCWBM was high fluidity and segregation resistance, which was similar to the workability requirement of self-consolidating concrete (SCC) [25]. The material composition of CCWBM in binders and aggregates was analogous to SCC too [26]. Therefore, slump flow test was carried out to evaluate the fluidity of CCWBM according to ASTM C1611-M14 “Standard Test Method for Slump Flow of Self-Consolidating Concrete” [27]. No superplasticizer was added in the first mixing of all mixtures. If slump was satisfied, SP of the mixture would be zero, or superplasticizer would be added until the slump was satisfied. Coarse adjustment is 10 g once, about 0.1% of binder, while fine adjustment is 5 g once, about 0.05% of binder. The adding method is selected according to the flow characteristics of fresh slurry.


## 2.1. Raw Materials

The investigated mixtures were systematically proportioned using coal gangue obtained from Xinyang Colliery, a mine in Shanxi Province of China. The samples were mechanically crushed and then categorized into two groups based on particle size, fine gangue aggregate with MSA of 5 mm and coarse gangue aggregate with MSA of 15 mm. The total gangue in each cubic filling slurry was 950 kg. The fineness modulusμ of the fine gangue aggregate was 3.02. A class F fly ash combined with ordinary Portland cement (CEM I 42.5N) (binary system) was used, and the integral dose of binder was 570 kg/m3. The main chemical components and physical properties of coal gangue, cement, and fly ash are summarized in Table 1 [7]. A naphthalene sulphonate-based superplasticizer in powder was incorporated in all mixtures to reach target slump.Table 1
Chemical and physical properties of coal gangue, fly ash, and cement [7].
Coal gangue
Fly ash
Cement
SiO2
28.46
52.42
22.36
Al2O3
16.11
32.48
5.53
Fe2O3
10.86
3.62
3.45
CaO
7.15
3.05
65.08
MgO
3.50
1.01
1.27
TiO2
0.80
1.26
—
Specific gravity (g/cm3)
2.0
2.2
3.1
Specific surface (m2/kg)
499
415
349
Fineness (>45μm) (%)
53.78
42.54
5
Moisture content (%)
8.0
0.56
—
Loss on ignition (%)
—
3.8
2


## 2.2. Test Methods

The required workability of CCWBM was high fluidity and segregation resistance, which was similar to the workability requirement of self-consolidating concrete (SCC) [25]. The material composition of CCWBM in binders and aggregates was analogous to SCC too [26]. Therefore, slump flow test was carried out to evaluate the fluidity of CCWBM according to ASTM C1611-M14 “Standard Test Method for Slump Flow of Self-Consolidating Concrete” [27]. No superplasticizer was added in the first mixing of all mixtures. If slump was satisfied, SP of the mixture would be zero, or superplasticizer would be added until the slump was satisfied. Coarse adjustment is 10 g once, about 0.1% of binder, while fine adjustment is 5 g once, about 0.05% of binder. The adding method is selected according to the flow characteristics of fresh slurry.


## 3. Establishment of RSM Model

### 3.1. Design of Response Surface

According to the model of Design-Expert, a second-order polynomial model was selected to fit the response:(1)Y=b0+∑i=1kbiXi+∑i=1kbiiXi2+∑i<jkbijXiXj+eX1,X2,…,X3,where Y was response; Xi was independent variable; bi,bii,andbij denoted regression coefficient of first degree item, second degree item, and cross degree item, respectively; k was the number of factors; and e was the error caused by test and regression [21, 28].The dosage of superplasticizer (SP) was selected as response in this study. Fly ash content, fine gangue ratio, and mass concentration were the key parameters in preparation of CCWBM. Their variation affected the mix proportion of CCWBM, thus directly affecting SP. Consequently, fly ash content, fine gangue ratio, and mass concentration were chosen as function factors, and tests of three-factor-three-level were designed. The levels of test factors are shown in Table2.Table 2
Levels of factors of RSM.
Factor
Code
Levels of code
−1
0
1
Fly ash content (kg/m3)
A
360
380
400
Fine gangue ratio (%)
B
27
30
33
Mass concentration (%)
C
79
80
81


### 3.2. Test Results

Test plan and results are shown in Table3. It was found that mass concentration had a significant influence on SP that SP significantly grew with the increase of mass concentration. When fine gangue ratio rose from 25% to 35%, SP hardly changed. SP tended to be larger with the increase of fly ash content. There was no remarkable bleeding in slump test for all mixtures because CCWBM contained a large amount of powder including fly ash with small particle size [29].Table 3
Design of tests based on CCD and test results.
Run
Design of tests
Results of tests
A
B
C
SP (% of binder)
Slump flow (mm)
VSI
1
1.000
1.000
1.000
0.702
440
0
2
−1.000
1.000
1.000
0.526
420
0
3
0.000
0.000
0.000
0.521
450
0
4
0.000
1.682
0.000
0.667
430
0
5
−1.682
0.000
0.000
0.281
430
0
6
1.000
−1.000
−1.000
0.075
470
1
7
0.000
0.000
1.682
1.253
420
0
8
0.000
0.000
−1.682
0.000
540
2
9
0.000
0.000
0.000
0.521
460
0
10
0.000
−1.682
0.000
0.596
460
0
11
0.000
0.000
0.000
0.521
445
0
12
0.000
0.000
0.000
0.521
450
0
13
−1.000
−1.000
1.000
1.003
465
0
14
1.000
−1.000
1.000
1.053
460
0
15
−1.000
1.000
−1.000
0.351
475
1
16
1.000
1.000
−1.000
0.251
500
1
17
−1.000
−1.000
−1.000
0.000
440
1
18
1.682
0.000
0.000
0.602
450
0
19
0.000
0.000
0.000
0.521
450
0
20
0.000
0.000
0.000
0.521
445
0


### 3.3. Fitting the Model

Setting SP as response, the polynomial regression model expressed as equation (2) which relates all the variables is calculated using Design-Expert software according to equation (1):(2)SI=17.69+1.14A−3.05B−5.23C−1.79BC+0.63A2+0.51B2+1.45C2.Table4 and 5 show the results of variances analysis for this model and significance tests for regression coefficients. The probability p value gained from ANOVA is relatively low (pmodel>F<0.0001) which means that the model is significant [24]. The determination coefficient, R2, is 0.9671, indicating that the model can explain response value change of 96.7% and only 3.29% of response variance cannot be explained by this model [24, 30]. Furthermore, predicted value and actual value are mainly in a straight line in Figure 1 [22]. All of above demonstrate that the model with a high precision can be used to SP analysis and prediction.Table 4
ANOVA of response surface quadratic model for SP.
Sum of squares
df
Mean square
F value
p value
Model
0.4303
6
0.0717
63.68
<0.0001
A
0.0091
1
0.0091
8.12
0.0137
B
0.0023
1
0.0023
2.07
0.1741
C
0.3467
1
0.3467
307.88
<0.0001
BC
0.0522
1
0.0522
46.39
<0.0001
A2
0.0081
1
0.0081
7.21
0.0187
C2
0.0135
1
0.0135
11.97
0.0042
Residual
0.0146
13
0.0011
Lack of fit
0.0146
8
0.0018
1.156
×
10
8
<0.0001
Pure error
7.916
×
10
−
11
5
1.583
×
10
−
11
Cor total
0.4449
19
7.916 ∗ 11
Standard deviation: 0.0336;R2: 0.9671; adjusted (R2): 0.9519; adequate precision: 27.8528.Table 5
Significant test of the regression coefficients.
Factor
Coefficient estimate
df
Standard error
95% CI low
95% CI high
VIF
Intercept
0.6490
1
0.0116
0.6239
0.6741
A
−0.0259
1
0.0091
−0.0455
−0.0063
1.0000
B
−0.0131
1
0.0091
−0.0327
0.0066
1.0000
C
−0.1593
1
0.0091
−0.1789
−0.1397
1.0000
BC
0.0808
1
0.0119
0.0552
0.1064
1.0000
A2
0.0236
1
0.0088
0.0046
0.0426
1.01
C2
0.0304
1
0.0088
0.0114
0.0494
1.01Figure 1
Predicted vs. actual. The predicted value and actual value are mainly in a straight line.


## 3.1. Design of Response Surface

According to the model of Design-Expert, a second-order polynomial model was selected to fit the response:(1)Y=b0+∑i=1kbiXi+∑i=1kbiiXi2+∑i<jkbijXiXj+eX1,X2,…,X3,where Y was response; Xi was independent variable; bi,bii,andbij denoted regression coefficient of first degree item, second degree item, and cross degree item, respectively; k was the number of factors; and e was the error caused by test and regression [21, 28].The dosage of superplasticizer (SP) was selected as response in this study. Fly ash content, fine gangue ratio, and mass concentration were the key parameters in preparation of CCWBM. Their variation affected the mix proportion of CCWBM, thus directly affecting SP. Consequently, fly ash content, fine gangue ratio, and mass concentration were chosen as function factors, and tests of three-factor-three-level were designed. The levels of test factors are shown in Table2.Table 2
Levels of factors of RSM.
Factor
Code
Levels of code
−1
0
1
Fly ash content (kg/m3)
A
360
380
400
Fine gangue ratio (%)
B
27
30
33
Mass concentration (%)
C
79
80
81


## 3.2. Test Results

Test plan and results are shown in Table3. It was found that mass concentration had a significant influence on SP that SP significantly grew with the increase of mass concentration. When fine gangue ratio rose from 25% to 35%, SP hardly changed. SP tended to be larger with the increase of fly ash content. There was no remarkable bleeding in slump test for all mixtures because CCWBM contained a large amount of powder including fly ash with small particle size [29].Table 3
Design of tests based on CCD and test results.
Run
Design of tests
Results of tests
A
B
C
SP (% of binder)
Slump flow (mm)
VSI
1
1.000
1.000
1.000
0.702
440
0
2
−1.000
1.000
1.000
0.526
420
0
3
0.000
0.000
0.000
0.521
450
0
4
0.000
1.682
0.000
0.667
430
0
5
−1.682
0.000
0.000
0.281
430
0
6
1.000
−1.000
−1.000
0.075
470
1
7
0.000
0.000
1.682
1.253
420
0
8
0.000
0.000
−1.682
0.000
540
2
9
0.000
0.000
0.000
0.521
460
0
10
0.000
−1.682
0.000
0.596
460
0
11
0.000
0.000
0.000
0.521
445
0
12
0.000
0.000
0.000
0.521
450
0
13
−1.000
−1.000
1.000
1.003
465
0
14
1.000
−1.000
1.000
1.053
460
0
15
−1.000
1.000
−1.000
0.351
475
1
16
1.000
1.000
−1.000
0.251
500
1
17
−1.000
−1.000
−1.000
0.000
440
1
18
1.682
0.000
0.000
0.602
450
0
19
0.000
0.000
0.000
0.521
450
0
20
0.000
0.000
0.000
0.521
445
0


## 3.3. Fitting the Model

Setting SP as response, the polynomial regression model expressed as equation (2) which relates all the variables is calculated using Design-Expert software according to equation (1):(2)SI=17.69+1.14A−3.05B−5.23C−1.79BC+0.63A2+0.51B2+1.45C2.Table4 and 5 show the results of variances analysis for this model and significance tests for regression coefficients. The probability p value gained from ANOVA is relatively low (pmodel>F<0.0001) which means that the model is significant [24]. The determination coefficient, R2, is 0.9671, indicating that the model can explain response value change of 96.7% and only 3.29% of response variance cannot be explained by this model [24, 30]. Furthermore, predicted value and actual value are mainly in a straight line in Figure 1 [22]. All of above demonstrate that the model with a high precision can be used to SP analysis and prediction.Table 4
ANOVA of response surface quadratic model for SP.
Sum of squares
df
Mean square
F value
p value
Model
0.4303
6
0.0717
63.68
<0.0001
A
0.0091
1
0.0091
8.12
0.0137
B
0.0023
1
0.0023
2.07
0.1741
C
0.3467
1
0.3467
307.88
<0.0001
BC
0.0522
1
0.0522
46.39
<0.0001
A2
0.0081
1
0.0081
7.21
0.0187
C2
0.0135
1
0.0135
11.97
0.0042
Residual
0.0146
13
0.0011
Lack of fit
0.0146
8
0.0018
1.156
×
10
8
<0.0001
Pure error
7.916
×
10
−
11
5
1.583
×
10
−
11
Cor total
0.4449
19
7.916 ∗ 11
Standard deviation: 0.0336;R2: 0.9671; adjusted (R2): 0.9519; adequate precision: 27.8528.Table 5
Significant test of the regression coefficients.
Factor
Coefficient estimate
df
Standard error
95% CI low
95% CI high
VIF
Intercept
0.6490
1
0.0116
0.6239
0.6741
A
−0.0259
1
0.0091
−0.0455
−0.0063
1.0000
B
−0.0131
1
0.0091
−0.0327
0.0066
1.0000
C
−0.1593
1
0.0091
−0.1789
−0.1397
1.0000
BC
0.0808
1
0.0119
0.0552
0.1064
1.0000
A2
0.0236
1
0.0088
0.0046
0.0426
1.01
C2
0.0304
1
0.0088
0.0114
0.0494
1.01Figure 1
Predicted vs. actual. The predicted value and actual value are mainly in a straight line.


## 4. Analysis of Test Results

Figures2–4 are contours and 3D images of the effects of fly ash content, fine gangue ratio, and mass concentration and their interactions on SP.Figure 2
Influence of A, B, and their interaction on SP.Figure 3
Influence of A, C, and their interaction on SP.Figure 4
Influence of B, C, and their interaction on SP.


### 4.1. Effect of Fly Ash Content

As shown in Figure2, SP gradually becomes large with the growth of fly ash content when the dosage of fly ash is less than 390 kg/m3. An aggregate space model is introduced to explain SP change and adjusted to be reliable to some extent [30].As illustrated in Figure5, water is the only flowable ingredient in fresh filling slurry. Water molecules enwrap cement and fly ash particles, forming a lubricating layer between them, which is the minimal unit of slurry flow and cement-fly ash paste. The larger the space between powder particles (defined as powder space), the better the fluidity of cement-fly ash paste [26]. Cement-fly ash paste surrounds fine gangue particles and forms a lubricating layer between them, which makes up the middle unit of slurry flow and mortar. The flowability of mortar depends on the space between fine gangue particles (defined as fine gangue space) and the fluidity of cement-fly ash paste. The better the fluidity of cement-fly ash paste, the lower the friction on fine gangue particles, the more excellent the flowability of mortar. The fluidity of mortar tends to be better with bigger fine gangue space. When the fine gangue space tends to infinity, the fluidity of mortar will be close to the fluidity of cement-fly ash paste [30]. Mortar enwraps coarse gangue particles and forms a lubricating layer between them, which forms the maximal unit of slurry flow. The flowability of fresh slurry relies on the space between coarse gangue particles (defined as coarse gangue space) and the fluidity of mortar. The better the fluidity of mortar, the lower the friction on coarse gangue particles, the more favourable the flowability of fresh slurry. The fluidity of fresh slurry tends to be better with larger coarse gangue space. When coarse gangue space tends to be infinite, the fluidity of fresh slurry will be close to the fluidity of mortar [30]. However, when the powder space is too large, there is so much free water in mixtures that the initial setting time of slurry is prolonged and the dry shrinkage of backfill body is high, which damages the strength and durability of backfill body. When the fine gangue space is too big, the viscosity of mortar is small and thus the segregation of fresh slurry is serious. The volume of coarse gangue is small and the strength of backfill body is low with large coarse gangue space. Therefore, filling slurry must enjoy moderate powder space, fine aggregate space, and coarse gangue space to gain favourable performance [29, 31].Figure 5
The aggregate space model for CCWBM.Because the particle size of fly ash is smaller than that of cement [28, 32], the amount of powder particles in mixtures increases with the growth of fly ash content and powder space decreases, which leads to the reduction of the flowability of cement-fly ash paste. Naphthalene sulphonate-based superplasticizer can be adsorbed on the surface of cement and fly ash particles and affects the zeta potential of powder particles. This prevents cement flocculation and reduces constructral water on the surface of powder particles [19, 33–35]. As a result, free water in mixtures grows and its distribution is optimized. Meantime, a solvent layer is formed on the surface of powder particles, which plays a good lubricating role. The above two effects increase powder space and therefore, with the growth of fly ash content, SP gradually increases to reach the target slump. Nevertheless, the variation of SP is opposite when the dosage of fly ash is greater than 390 kg/m3. Because the mass of cement decreases, fly ash can play a better role in dispersing cement particles [36, 37]. Moreover, as the surface electrical properties of fly ash is different from cement, cement flocculation and bound water decrease. These effects ensure that mixtures have a moderate initial powder space, so SP becomes small.


### 4.2. Effect of Mass Concentration

As can be seen from Figure3, SP significantly grows with the increase of mass concentration. Because of the reduction of mixing water, powder space becomes small. It is necessary to enlarge the dosage of superplasticizer to reach large powder space.


### 4.3. Effect of Fine Gangue Ratio

It can be found from Figure3 that increasing fine gangue ratio enlarges SP when mass concentration is 79% because the growth of fine gangue volume leads to the reduction of fine aggregate space. Adding superplasticizer can enlarge powder space and therefore improve the fluidity of cement-fly ash paste and increase its volume. The increase of cement-fly ash paste volume can enlarge the fine aggregate space and thus improve the fluidity of mortar. However, when mass concentration is 81%, the variation of SP is opposite because compared with mass concentration of 79%, the reduction of mixing water is significant. The increase of fine gangue volume will cause the increase of mortar volume and the reduction of coarse gangue, which will enlarge coarse gangue space. The variation of SP with fine gangue ratio is affected by mass concentration, indicating that the interaction between fine gangue ratio and mass concentration is significant.


### 4.4. Rank of Significance

The rank of the factors’ significance for SP is mass concentration > fly ash content > fine gangue ratio, and the curves on the 3D response surface change gradually from steep to gentle. Mass concentration affects SP with steep curve on the 3D response surface, while the influence of fly ash content on it is weak with gentle curve. This is also demonstrated in Table4 where the p value of C is less than 0.0001 [22, 36].


### 4.5. Interaction

Contour shape can reflect the strength of the interaction effect. The oval shape shows that the two factors interact significantly, while circular indicates the opposite [22]. Therefore, the interaction between fly ash content and fine gangue ratio is significant. However, the contour shape of BC is neither circular nor oval, and the 3D response surface is obviously distorted. In addition, the p value of BC is less than 0.0001 as shown in Table 4, so the interaction between fine gangue ratio and mass concentration is the most significant [37].


## 4.1. Effect of Fly Ash Content

As shown in Figure2, SP gradually becomes large with the growth of fly ash content when the dosage of fly ash is less than 390 kg/m3. An aggregate space model is introduced to explain SP change and adjusted to be reliable to some extent [30].As illustrated in Figure5, water is the only flowable ingredient in fresh filling slurry. Water molecules enwrap cement and fly ash particles, forming a lubricating layer between them, which is the minimal unit of slurry flow and cement-fly ash paste. The larger the space between powder particles (defined as powder space), the better the fluidity of cement-fly ash paste [26]. Cement-fly ash paste surrounds fine gangue particles and forms a lubricating layer between them, which makes up the middle unit of slurry flow and mortar. The flowability of mortar depends on the space between fine gangue particles (defined as fine gangue space) and the fluidity of cement-fly ash paste. The better the fluidity of cement-fly ash paste, the lower the friction on fine gangue particles, the more excellent the flowability of mortar. The fluidity of mortar tends to be better with bigger fine gangue space. When the fine gangue space tends to infinity, the fluidity of mortar will be close to the fluidity of cement-fly ash paste [30]. Mortar enwraps coarse gangue particles and forms a lubricating layer between them, which forms the maximal unit of slurry flow. The flowability of fresh slurry relies on the space between coarse gangue particles (defined as coarse gangue space) and the fluidity of mortar. The better the fluidity of mortar, the lower the friction on coarse gangue particles, the more favourable the flowability of fresh slurry. The fluidity of fresh slurry tends to be better with larger coarse gangue space. When coarse gangue space tends to be infinite, the fluidity of fresh slurry will be close to the fluidity of mortar [30]. However, when the powder space is too large, there is so much free water in mixtures that the initial setting time of slurry is prolonged and the dry shrinkage of backfill body is high, which damages the strength and durability of backfill body. When the fine gangue space is too big, the viscosity of mortar is small and thus the segregation of fresh slurry is serious. The volume of coarse gangue is small and the strength of backfill body is low with large coarse gangue space. Therefore, filling slurry must enjoy moderate powder space, fine aggregate space, and coarse gangue space to gain favourable performance [29, 31].Figure 5
The aggregate space model for CCWBM.Because the particle size of fly ash is smaller than that of cement [28, 32], the amount of powder particles in mixtures increases with the growth of fly ash content and powder space decreases, which leads to the reduction of the flowability of cement-fly ash paste. Naphthalene sulphonate-based superplasticizer can be adsorbed on the surface of cement and fly ash particles and affects the zeta potential of powder particles. This prevents cement flocculation and reduces constructral water on the surface of powder particles [19, 33–35]. As a result, free water in mixtures grows and its distribution is optimized. Meantime, a solvent layer is formed on the surface of powder particles, which plays a good lubricating role. The above two effects increase powder space and therefore, with the growth of fly ash content, SP gradually increases to reach the target slump. Nevertheless, the variation of SP is opposite when the dosage of fly ash is greater than 390 kg/m3. Because the mass of cement decreases, fly ash can play a better role in dispersing cement particles [36, 37]. Moreover, as the surface electrical properties of fly ash is different from cement, cement flocculation and bound water decrease. These effects ensure that mixtures have a moderate initial powder space, so SP becomes small.


## 4.2. Effect of Mass Concentration

As can be seen from Figure3, SP significantly grows with the increase of mass concentration. Because of the reduction of mixing water, powder space becomes small. It is necessary to enlarge the dosage of superplasticizer to reach large powder space.


## 4.3. Effect of Fine Gangue Ratio

It can be found from Figure3 that increasing fine gangue ratio enlarges SP when mass concentration is 79% because the growth of fine gangue volume leads to the reduction of fine aggregate space. Adding superplasticizer can enlarge powder space and therefore improve the fluidity of cement-fly ash paste and increase its volume. The increase of cement-fly ash paste volume can enlarge the fine aggregate space and thus improve the fluidity of mortar. However, when mass concentration is 81%, the variation of SP is opposite because compared with mass concentration of 79%, the reduction of mixing water is significant. The increase of fine gangue volume will cause the increase of mortar volume and the reduction of coarse gangue, which will enlarge coarse gangue space. The variation of SP with fine gangue ratio is affected by mass concentration, indicating that the interaction between fine gangue ratio and mass concentration is significant.


## 4.4. Rank of Significance

The rank of the factors’ significance for SP is mass concentration > fly ash content > fine gangue ratio, and the curves on the 3D response surface change gradually from steep to gentle. Mass concentration affects SP with steep curve on the 3D response surface, while the influence of fly ash content on it is weak with gentle curve. This is also demonstrated in Table4 where the p value of C is less than 0.0001 [22, 36].


## 4.5. Interaction

Contour shape can reflect the strength of the interaction effect. The oval shape shows that the two factors interact significantly, while circular indicates the opposite [22]. Therefore, the interaction between fly ash content and fine gangue ratio is significant. However, the contour shape of BC is neither circular nor oval, and the 3D response surface is obviously distorted. In addition, the p value of BC is less than 0.0001 as shown in Table 4, so the interaction between fine gangue ratio and mass concentration is the most significant [37].


## 5. Conclusions

The SP model of CCWBM build in this paper is fitting well and thereby could be applied to analyze and predict the dosage of superplasticizer of CCWBM. As the test results illustrate, SP rises significantly with the increase of mass concentration and tends to be larger with bigger fly ash content. The effect of sand ratio on SP is related to mass concentration. The rank of the factors’ significance for SP is mass concentration > fine gangue ratio > fly ash content, and the curves on the 3D response surface change gradually from steep to gentle. The interaction between mass concentration and fine gangue ratio is the most remarkable. Moreover, a reasonable explanation of the variation of SP is made through using the improved aggregate space model and thus it could be used to analyze the fluidity of CCWBM. However, the SP model of CCWBM is built based on the results of slump flow test. As the properties of CCWBM have been greatly affected by raw materials and material composition, the model in the present paper needs to be revised and improved.



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*Source: 5328523-2019-01-20.xml*