Study on Slump and Compressive Strength of Gangue Based on Aggregate Size Gradation

Abstract

In order to solve the ecological environment pollution caused by a large amount of coal gangue accumulation and the problems of poor conveying performance and low support strength of paste filling materials. Based on the standard slump test and uniaxial compressive strength test, the slump and compressive strength (post-coagulation) of gangue paste under different aggregate size aggregations were obtained through orthogonal experiments in this study. The results show that the slump of the gangue filling paste with four types of aggregate size gradations is negatively correlated with the mass fraction, and the slump of the filling paste with a coarser aggregate content is more obviously affected by the mass fraction The increase of fine aggregate content has a significant impact on the compressive strength of the filling paste, which shows a trend of first increasing and then decreasing. When the mixing ratio of coarse aggregate and fine aggregate is 5:5, the compressive strength of the paste reaches the best. In addition, different proportions of aggregate mixing cause the filling paste to form different skeleton structures, including the skeleton void structure at 7:3 or 6:4, the skeleton dense structure at 5:5, and the skeleton suspension structure at 4:6, which are decisive for the final performance of the paste. By analyzing the experimental results of the compressive strength and slump of the gangue filling paste, it was found that the relationship between the compressive strength and slump of the gangue filling paste is a power index function. Through data fitting, it was found that the regression coefficient of the fitting function is no less than 0.97, and the fitting effect is good for evaluating the strength of the filling paste under the aggregate size grading.

1. Introduction

According to incomplete statistics, the annual discharge of coal gangue in China has reportedly reached 759 million tons [1] and has continued to increase annually. Addressing gangue is a significant concern in the coal mining industry [2,3]. The utilization of gangue filling has the potential to efficiently manage waste coal gangue on a significant scale, enhance the working environment within the stope, mitigate ground collapse, and enhance mining productivity. Consequently, gangue incorporation has emerged as a crucial technology in the context of environmentally sustainable mining [4,5,6,7].

Compared with traditional dry filling, water–sand filling, and tailing consolidation filling technology, paste filling should have the following advantages: no stratification, no segregation, no precipitation, uniform strength distribution, and reduce the need for cement consumption, and the vast majority of mines adopt paste-filling technology [8]. However, with the increasing depth of coal mining, structural filling with a low filling rate in the goaf puts forward higher requirements for the filling strength of the backfill body [9,10]. The slump test is a subjective evaluation method for fluidity tests. The accuracy of calculating the yield stress using the theoretical model still needs to be verified. Currently, the test methods for paste slurry fluidity include the slump test, viscometer, L-shaped tube test, and loop tube test [11,12,13,14,15]. A rheometer is commonly used in the laboratory to test the rheological properties of the tailing slurry, and pressure test instruments are used to test the compressive strength of the paste. However, most mine sites do not have such testing conditions. Therefore, if the relationship between the collapse of the gypsum body and the compressive strength of the paste can be established, it can provide a new way to quickly and accurately evaluate the filling strength of the paste. Murate [16] conducted a stress analysis on the slump cone test for concrete mortar and, for the first time, established a relationship model between the slump of concrete mortar in a cone and the yield stress. Based on the Murate model theory, Liang et al. [17] constructed a simplified formula for dimensionless models of conical and cylindrical cave-in cylinders. Tanigawa [18] used the finite element analysis method to study the flow model of fresh concrete slurry, which was considered a Bingham model. He analyzed the relationship between the flow properties and the collapse of the concrete slurry. The results show a strong correlation between the yield stress and slump, whereas the correlation between the viscosity and slump was weak. Elizabeth et al. [19] explored the effects of saline groundwater or seawater as mix water in cemented fills on the rheological properties (ability to control flow or transportability) and setting time of the cemented backfill. Wu et al. [20] studied the influence of slurry rheometer test method on the yield stress of the whole tailings paste material and compared the dimensionless yield stress calculated by slump with the yield stress measured by rheometer.

In this paper, the influence of different mass fraction and aggregate ratio on flowing property and uniaxial compressive strength of filling paste was explored through detailed testing and exploration of 4 aggregates with unique particle size ratios, standard slump testing, and uniaxial compressive strength testing. In addition, we have developed a set of mathematical models that accurately reflect the slump and compressive strength of filling paste under different aggregate size gradations. This innovative research result not only provided more robust filling process parameters for mine safety production, but also provided valuable practical reference and decision-making basis for other mines in the same industry.

2. Experimental Material

2.1. Gangue Paste Aggregate

The color of coal gangue, which is the primary component associated with the coal formation process, is black, as indicated in

Table 1. Chemical composition of coal gangue.

Compound	SiO2	Al2O3	Na2O	MgO	K2O	CaO	Fe2O3	Other
content%	52.81	22.35	1.18	1.21	1.33	1.64	5.12	14.36

. Gangue mainly contains SiO₂, Al₂O₃, and other ingredients as well as some trace elements. Figure 1 shows coal gangue.

Gangue is primarily categorized into two groups: coal washing gangue and coal driving gangue. The gangue used in this experiment was sourced from the washed gangue of a mine located in Hebei Province. Given the significant impact of gangue aggregate grade on filling material performance, it is essential to utilize a jaw crusher to crush the gangue prior to the experiment to attain the specified aggregate particle size (<25 mm) [21]. The grading of experimental gangue aggregate is shown in

Table 2. Particle size grading of gangue.

Category	Fine Particle Size Gangue Aggregate	Coarse Particle Size Gangue Aggregate
Particle size/mm	0.3–5 mm	5–25 mm

. The particle size distribution of gangue is shown in Figure 2, and the particle size of gangue particles is mainly distributed within the range of 5–10 mm.

2.2. Gangue Paste Auxiliary Material

Fly ash possesses activation and excitation properties, making it suitable for replacing a portion of fine aggregates in filling materials. The addition of an appropriate amount of fly ash can decrease pipeline transport resistance and enhance the pumping performance of the slurry. Therefore, fly ash is commonly used as an auxiliary material in traditional gangue-filling pastes. However, considering the high demand and cost of fly ash in traditional gangue filling paste materials, Li et al. [22] conducted a study on the feasibility of using gangue powder as a substitute for fly ash in filling materials. The results indicated that with a water content of 23% and cement material content of 15%, the filling materials achieved an early compressive strength of 0.743 MPa while maintaining satisfactory fluidity. The compressive strength at 28 days was 4.87 MPa, which matches the compressive strength of the backfill. Therefore, this study used gangue powder instead of fly ash as an alternative supplementary material for filling materials.

2.3. Cementing Agent

The use of a binder determines the final paste-filling strength. Yan [23] obtained the optimal binder ratio through an experimental design of 70% slag powder, 25% cement clinker, and 5% desulfurized gypsum.

2.3.1. Slag Powder

Slag powder is an industrial waste material that is produced during metal refining. It has the ability to chemically react with OH- under alkaline conditions, which enhances its mechanical properties and strengthens the material. In addition, the presence of slag can accelerate the hydration reaction of cement clinker, resulting in the faster production of hydration products. This, in turn, improved the mechanical properties of the cemented body.

2.3.2. Cement Clinker

Cement clinker is primarily produced by grinding, sintering, and cooling limestone and iron raw materials. It exhibits high activity and reacts with water to generate an alkaline solution containing Ca(OH)₂. This solution stimulates the reaction of other active substances and accelerates the overall reaction.

2.3.3. Flue Gas Desulfurization Gypsum

Desulfurized gypsum plays an important role in gel materials. When it comes into contact with water, it reacts with the active substance in the cement clinker and slag powder to form needle-like crystals of high-sulfur hydrated calcium sulfoaluminate, known as ettringite (AFt). This promotes gel formation in the backfill and early strength development.

3. Experimental

3.1. Experimental Design

3.1.1. Talbot Theory

One of the ways to optimize the grain size gradation of gangue is to apply Talbot theory, which provides a method for calculating and designing aggregate gradation. By means of Talbot theory, the appropriate proportion of particles of different sizes can be determined to achieve maximum density and minimum porosity, thereby improving the compaction degree and compressive strength of the backfill. In practical application, this method can simplify the grading design process by drawing the maximum density curve in semi-logarithmic coordinates and determining the content proportion of each particle size according to this curve. In this way, the physical properties of backfill can be effectively improved and its application in mine engineering can be enhanced.

Talbot’s formula:

$$T_x=[{d/D]}^K$$

(1)

where T_x is the passing rate of aggregate particle size d, %; d is the current aggregate particle size; D is the maximum aggregate particle size, mm; K is the Talbot coefficient.

According to Talbot’s formula, the particle size composition of gangue aggregate with different K values (0.3, 0.4, 0.5, 0.6) is taken, and the passing rate of gangue aggregate in each screen is shown in

Table 3. Aggregate size grading table.

Value of K	Mass Ratio/%		Approximate Ratio
	0.05–5 mm	5–25 mm
0.3	0.62	0.38	6:4
0.4	0.53	0.47	5:5
0.5	0.44	0.56	4:6
0.6	0.38	0.62	3:7

. Therefore, four different aggregate gradations were selected in this paper; namely, the ratio of coarse aggregate to fine aggregate was 6:4, 5:5, 4:6, and 7:3.

3.1.2. Orthogonal Experimental Design

In this experiment, gangue powder was used as an auxiliary material instead of fly ash (with a general diameter of 0.05–0.3 mm). Gangue particles with a diameter of 0.3–25 mm were used as the aggregate, and a mixture of slag powder, desulfurized gypsum, and cement clinker was used as the cementing agent. On this basis, the ratio of auxiliary materials to aggregate was kept constant at 3:7, and the dosage of the cement clinker remained unchanged at 8%, as shown in

Table 4. Filling material composition ratio.

Materials	Gangue Powder	Gangue Aggregate	Cementing Agent
content%	27.6%	64.4%	8%

The relationship between the slump and compressive strength of gangue paste was established by varying the ratio of fine aggregate to coarse aggregate and the mass fraction of the gangue paste. Therefore, in this study, based on Talbot theory, the ratios of coarse aggregates to fine aggregates were selected as 7:3, 6:4, 5:5, and 4:6. The gangue mass fractions were selected as 78%, 80%, 82%, and 84% for the test. The test process is illustrated in Figure 3.

An orthogonal test method was adopted in the experiment [24]. Orthogonal experimental methods are efficient, comprehensive, and systematic experimental methods. Through a balanced combination of experimental conditions and a standardized process, it can comprehensively evaluate the impact of multiple factors and their interaction effects on the results in a small number of experiments. At the same time, it is convenient for statistical analysis and comparison of results, which helps to optimize experimental conditions, predict system behavior, and simplify the solution of complex problems. In this experiment, a two-factor, four-level orthogonal test table, L16 (4²), was used for the experimental design. The orthogonal test scheme is shown in

Table 5. Orthogonal experiment table.

Level	Factor
	A%	B
1	78	7:3
2	80	6:4
3	82	5:5
4	84	4:6

where A represents the mass fraction of the filling paste, and B represents the ratio of coarse aggregate to fine aggregate.

.

3.2. Experimental Method

According to the orthogonal experimental design, 16 groups of filling slurries with different proportions were prepared. To mitigate the impact of testing errors, the average value for each group was calculated three times. After preparing the filling slurry, it was poured into a 100 mm × 100 mm × 100 mm cube mold that had been coated with release oil. Each group consisted of 4 specimens. After the release, the specimens were placed in a curing box at a temperature of 20 ± 2 °C and relative humidity of 95 ± 1%. The 4 test specimens in each group were cured in the curing box for 1 d, 3 d, 7 d, and 28 d, respectively, to reach the test age.

3.2.1. Standard Slump Test Procedure

The slump test was performed using a standard slump bucket with the following specifications: top diameter of 100 mm, bottom diameter of 200 mm, and height of 300 mm. The slump test is based on the provisions of the “Standard for Experimental Method of Performance of Ordinary Concrete Mix” (GB/T50080-2016) [25]. The testing process is illustrated in Figure 4.

3.2.2. Uniaxial Compressive Strength Test

The uniaxial compressive strength test was based on the GB/717767-1999 “Experimental Method for Mechanical Properties of Concrete.” [26] When the experimental block reached the testing age, we used a microcomputer-controlled electronic universal testing machine model WDW-100 to apply a continuous and uniform load at a speed of 0.1 mm/s until the experimental block was destroyed. We then recorded the failure load and peak ore pressure strength.

4. Experimental Results and Analysis

4.1. Experimental Results

To ensure the accuracy and repeatability of the test, each group of tests was repeated thrice to calculate the average value, which was then used as the final test result. The slump and yield stress measurements are listed in

Table 6. Orthogonal test results.

Test Group Number	Mass Fraction/%	Coarse–Fine Aggregate Ratio	Uniaxial Compressive Strength/MPa				Slump/mm
			1 d	3 d	7 d	28 d
1	78	7:3	0.14	1.23	2.37	2.52	257
2	78	6:4	0.37	1.97	2.27	2.78	238
3	78	5:5	0.63	2.91	3.17	3.35	225
4	78	4:6	0.54	2.61	2.85	3.16	216
5	80	7:3	0.18	1.52	2.67	2.86	223
6	80	6:4	0.45	2.31	2.68	3.17	215
7	80	5:5	0.70	2.56	3.45	3.67	210
8	80	4:6	0.62	2.38	3.17	3.31	202
9	82	7:3	0.28	2.08	3.01	3.21	203
10	82	6:4	0.55	2.71	3.36	3.38	196
11	82	5:5	0.82	3.19	3.65	3.81	191
12	82	4:6	0.69	2.97	3.34	3.58	189
13	84	7:3	0.38	2.24	3.39	3.77	184
14	84	6:4	0.64	3.06	3.68	4.01	178
15	84	5:5	0.91	3.84	4.43	4.73	175
16	84	4:6	0.79	3.46	3.86	4.33	171

.

4.2. Analysis of Slump Test Results of Aggregate Size Gradation

During the filling process, filling paste slurry is usually transported by either artesian flow or pumping. Therefore, the filling paste must have a certain level of fluidity, and the slump is an important indicator. If the slump is extremely large, the slurry is prone to segregation. Conversely, if the slump is too small, it becomes difficult for the slurry to flow normally, particularly in a pump. To meet the flow performance requirements of the filling paste, the slump of the filling paste is generally required to be between 180 and 240 mm.

As shown in Figure 5, the slump of the filling paste continuously decreased with a gradual increase in the proportion of fine aggregates. First, an increase in fine aggregate reduces the gap in the filling paste slurry, resulting in a more compact filling paste and reduced slump. Second, increasing the amount of fine aggregates increases the contact area between the aggregates, which in turn increases the internal friction force of the filling paste and reduces its fluidity. Therefore, an increase in this friction force resulted in a decrease in the slump of the filling paste. Furthermore, an increase in fine aggregates results in enhanced water absorption of the filling paste slurry, causing the free water in the slurry to transition into the adsorbed state. Consequently, the fluidity and plasticity of the filling paste decreased, leading to a reduction in its slump.

4.3. Relationship between Slump of Filling Paste and Mass Fraction

Figure 6 shows the relationship between the slump and mass fraction of gangue filling pastes with four different aggregate gradations. The results showed that the slump of the four filling pastes was negatively correlated with the mass fraction. Equation (2) was used for the linear fitting of the slump to mass fraction, and the fitting parameters are listed in Table 5. The p-value represents the significance in

Table 7. Linear fitting parameters of slump–mass fraction curve.

Paste Type	a1	b1	R2	p
Coarse–fine aggregate ratio 7:3	−11.95	1184.7	0.98	1.353 × 10 −4
Coarse–fine aggregate ratio 6:4	−9.55	1012.7	0.99	1.345 × 10 −2
Coarse–fine aggregate ratio 5:5	−8.45	884.7	0.99	4.989 × 10 −5
Coarse–fine aggregate ratio 4:6	−7.4	793.9	0.99	2.712 × 10 −4

.

$$H_0=a_1{C}_{w\mathrm{\%}}+b_1$$

(2)

where is H₀ slump; C_w%is the mass fraction, %; a₁ is the slope; b₁ is the intercept;

The results showed that the slump of the filling paste gradually decreased with an increase in the fine aggregate. For instance, within the range of 78–84% mass fraction, when the ratio of coarse aggregate to fine aggregate was 7:3, the slump of the filling paste decreased from 257 mm to 184 mm, resulting in a decrease of 28.4%. When the ratio of coarse aggregate to fine aggregate was 4:6, the slump of the filling paste decreased from 217 to 171 mm, a reduction of only 21.1%. The above results show that the slump of the coarse aggregate filling slurry was more significantly affected by the mass fraction.

Figure 6. Relationship between slump and mass fraction.

Figure 6. Relationship between slump and mass fraction.

4.4. Analysis of Compressive Strength Results of Aggregate Size Gradation

Figure 7 shows the experimental results of compressive strength of filling paste test blocks at ages of 1 d, 3 d, 7 d, and 28 d.

The compressive strength of the filling paste is a key factor in determining its stability. As shown in Figure 7, with a decrease in coarse aggregate and an increase in fine aggregate, the compressive strength of the filling paste test blocks at different ages increased. First, the voids within the paste were reduced when the amount of fine aggregate was increased. This leads to an increase in the cohesion and viscosity of the paste, ultimately resulting in an increase in its yield stress. Second, when the ratio of coarse aggregate to fine aggregate ranges from 7:3 to 5:5, the skeleton structure of the paste transitions from a framework-pore structure to a framework-dense structure, as shown in Figure 8a,b. This structure is formed because the gangue auxiliary material is adsorbed around the fine aggregate, which is then surrounded by the coarse aggregate. Coarse aggregates interlock with each other, creating a relatively stable spatial skeleton. When the ratio of coarse aggregate changed from 5:5 to 6:4, the yield stress of the paste test block decreased. This is because the proportion of coarse aggregates is reduced, and the proportion of fine aggregates increases. As a result, the internal structure of the paste changed from a framework-dense structure to a suspension-dense structure, as shown in Figure 8c.

4.5. Relationship between Slump and Yield Stress

Figure 9 shows the relationship between the slump and compressive strength of the filling pastes with different particle size gradations. In general, it was found that the slump of the paste has a power function relationship with the compressive strength of the paste test block at 28 days of age, and the regression coefficients after fitting with the power function model are no less than 0.97, which indicates a good fitting. The relationship between the slump and compressive strength of the filling paste is shown in Equation (3). Equation (4) is obtained by substituting Equation (2) into equation. The fitting parameters are listed in Table 8.

$${\tau }_y=a_2{{\mathrm{H}}_0}^{{\mathrm{b}}_2}$$

(3)

Enter the Equation (2) to obtain:

$${\tau }_y=a_2{{(a}_1{C}_{w\%}+b_1)}^{{\mathrm{b}}_2}$$

(4)

where ${\tau }_y$ is the compressive strength; a₂ and b₂ are constant.

Figure 9. Relationship between compressive strength and slump of 28-day filling paste.

Figure 9. Relationship between compressive strength and slump of 28-day filling paste.

Table 8. Parameters of the yield stress-slump fitting curve.

Paste Type	a2	b2	R2	p
Coarse–fine aggregate ratio 7:3	2325.43	−1.24	0.98	4.551 × 10 −4
Coarse–fine aggregate ratio 6:4	2355.85	−1.23	0.97	4.831 × 10 −4
Coarse–fine aggregate ratio 5:5	5079.57	−1.35	0.97	3.749 × 10 −4
Coarse–fine aggregate ratio 4:6	6288.95	−1.42	0.97	6.013 × 10 −4

Table 8. Parameters of the yield stress-slump fitting curve.

Paste Type	a2	b2	R2	p
Coarse–fine aggregate ratio 7:3	2325.43	−1.24	0.98	4.551 × 10 −4
Coarse–fine aggregate ratio 6:4	2355.85	−1.23	0.97	4.831 × 10 −4
Coarse–fine aggregate ratio 5:5	5079.57	−1.35	0.97	3.749 × 10 −4
Coarse–fine aggregate ratio 4:6	6288.95	−1.42	0.97	6.013 × 10 −4

The model is suitable for filling paste slurries with different aggregate size gradations that are mixed with water and cement. In this study, only four pastes with different aggregate size ratios are compared. Therefore, it is necessary to conduct slump and compressive strength tests on filling pastes of various particle size gradations. This will help verify the suitability of the model and determine the range of constant terms for predicting the yield stress in pastes with different particle size gradations. These empirical parameters are valuable for practical application. In addition, it is necessary to study the influence of the binder on the parameters of the model to further optimize the parameter model.

5. Conclusions

Based on the background of underground filling materials in coal mining, this paper measured the slump and compressive strength of the filling paste for gangue filling paste with different aggregate particle size gradations through orthogonal test, and reached the following conclusions:

(1) With the increase of the proportion of fine aggregate, the void inside the filling paste is significantly reduced, which makes the paste structure become denser, and this change leads to the slump of the filling paste.

(2) The slump of the filling paste was negatively correlated with the mass fraction for the four aggregate gradations. When the ratio of coarse aggregate to fine aggregate was 7:3, the slump of the filling paste decreased from 257 mm to 184 mm, representing a decrease of 28.4%. When the ratio of coarse aggregate to fine aggregate was 4:6, the slump of the filling paste decreased from 217 to 171 mm, a reduction of only 21.1%. The results showed that the filling paste with a higher mass fraction of coarse aggregate content was more significantly affected.

(3) When the ratio of coarse aggregate to fine aggregate was 7:3 or 6:4, the filling paste primarily formed a skeleton structure with a framework pore structure. When the ratio of coarse aggregate to fine aggregate was 5:5, the skeleton structure of the filling paste became framework-dense. The ratio of coarse aggregate to fine aggregate was 4:6, and the internal structure of the filling paste was suspended-dense.

(4) There is a power index function relationship between compressive strength and slump of filling paste with different aggregate particle size gradations. The fitting regression coefficient of this relationship is no lower than 0.97, and the fitting effect is good, which is suitable for evaluating the filling strength of filling paste with aggregate particle size gradation, and provides a certain reference value for studying the relationship between compressive strength and slump of filling paste.