Study on Correlations between Tailings Particle Size Distribution and Rheological Properties of Filling Slurries

Abstract

The influence of the mass concentration and particle size distribution on rheological parameters and slump was investigated by analyzing the mixture of overflow tailings (OT) and classified tailings (CT). The correlation between the rheological parameters, slump and characteristic value of the tailings particle diameter was discussed. Finally, the ratio parameters of a mixed tailings filling slurry were optimized using a lead–zinc mine in Guangdong, China as the engineering background. The results showed a quadratic decrease in the slump of the tailings slurry as the mass concentration increased, while the slump decreased with a decreasing particle size. With the increase in the mass concentration, the yield stress of the tailings slurry follows a quadratic function, while the plastic viscosity exhibits linear growth. The influence of tailings fine particles on the sensitivity of the yield stress and plastic viscosity to the mass concentration is reduced as their content increases. The yield stress and plastic viscosity of the tailings slurry exhibit a quadratic function decrease and linear growth as the slump increases. The slump of the tailings slurry is related to the particle size characteristic value and the mass concentration of the slurry. The correlation coefficient between the yield stress and the aggregate characteristic particle size increases most obviously at d₁₀~d₅₀, and the increase in the characteristic particle size will enhance the correlation between the yield stress and particle gradation. The correlation coefficient between the plastic viscosity and aggregate particle gradation parameters exhibits an initial increase followed by stabilization with an increasing characteristic particle size, with the most significant increase observed at d₁₀~d₅₀.

1. Introduction

With the continuous development of the global economy and increasing resource consumption, the exploitation of metal mine resources has been on a steady rise. The extraction of valuable minerals from extracted ores results in the generation of a significant volume of tailings. According to statistics, the global annual production of tailings exceeds 14 billion tons [1,2]. For the disposal of tailings in the mine, the conventional approach primarily involves storing a portion of the tailings as a slurry, with a mass fraction ranging from 10% to 30% in a designated tailings reservoir, while another portion is mixed with specific proportions of cementitious materials for filling underground goafs. The filling mining method poses challenges in achieving a harmonious balance between mining and filling and fails to effectively mitigate the disasters caused by tailings reservoirs [3,4]. In order to mitigate the risk posed by the tailings reservoirs, the extracted waste rock is crushed to a specific particle size and utilized as a construction material. The ultra-fine tailings discharged to the tailings reservoir are concentrated to a high concentration tailings slurry with a mass concentration of about 65%. The hydraulic characteristics of the ultra-fine tailings slurry can be modified by incorporating a certain proportion of graded tailings to satisfy the requirements for underground non-cemented filling. The slurry of mixed tailings is discharged into the void created by mining waste rock. This method can effectively mitigate the risk associated with tailings reservoirs [5,6]. The success of underground backfilling largely depends on the pumpability and fluidity of the tailings slurry. The rheological properties of paste describe the physical process of liquid flow and deformation. The relationship between the shear strength and shear rate is usually described by the variation in the shear strength with the shear rate and fitted by relevant rheological models. The relationship between the shear strength and shear rate is characterized by the yield stress and plastic viscosity [7,8,9]. The selection of pumping equipment or self-flow characteristics is determined by the calculation of the rheological properties of the slurry. The impact of the tailings particle size distribution on rheological parameters should not be underestimated. Accurate testing of rheological parameters for the tailings slurry is crucial in designing a filling system and achieving successful tailings filling [10,11,12,13,14].

Many scholars have conducted extensive research on the rheological characteristics of the tailings slurry. Chen investigated the influence of tailings particle gradation on the rheological properties of a cement steel slag-based composite filling slurry and pointed out that the extension of the tailings grinding time will greatly improve the yield stress of the slurry [15]. Zhou et al. carried out a study on the relationship between the slump and yield stress of a tailings slurry with different particle sizes and concluded that there was an exponential relationship between the slump height and yield stress [16]. Zhang et al. carried out an experimental study on the evolution law of the yield stress of tailings paste and obtained a significant DoseResp function relationship between the slurry concentration and yield stress [17]. Liu explored the influence of temperature on the rheological properties of a paste filling slurry and concluded that the yield stress of a low-concentration slurry decreased with the increase in temperature, while the yield stress of a high-concentration slurry increased first and then decreased with the increase in temperature [18]. Li et al. carried out a study on the yield stress variability behavior of unclassified tailings paste under the two-factor “shear time–shear rate” and pointed out that the peak yield stress and static yield stress are proportional to the shear rate, and the dynamic yield stress is inversely proportional to the shear time [19]. Zhang et al. carried out research on the rheological properties and yield stress model of a high-concentration slurry of waste rock-tailings and concluded that the high-concentration slurry of waste rock-tailings belongs to a yield-pseudoplastic body. The effect of cement addition on yield stress is more significant, and there is a quantitative relationship between the yield stress and water–cement ratio and aggregate volume fraction [20]. Ruan et al. studied the effect of flocculation sedimentation on the yield stress of a concentrated ultrafine tailings slurry and pointed out that flocculation sedimentation had a significant effect on the yield stress of a concentrated ultrafine tailings slurry [21]. Chen et al. studied the effect of anionic polyacrylamide (APAM) on the rheological properties of paste and pointed out that the presence of APAM significantly increased the yield stress and viscosity of a paste slurry [22]. Jiang et al. carried out a study on the rheological properties of the paste prepared by hemi-hydrate phosphogypsum and tailings and pointed out that the rheological stability gradually deteriorated with time, especially in the resting state [23]. Yan et al. studied the rheological properties and wall slip characteristics of tailings–waste rock cemented paste and pointed out that CTWB is a yield plastic fluid, and the shear thickening phenomenon occurs when the solid content is 67% and 69%, respectively. The critical shear rate value increases gradually with the increase in the mass concentration, and the yield stress decreases linearly with the increase in the coarse aggregate content [24]. Yue et al. studied the rheological properties of a coal tailings slurry and found that the yield stress of the paste slurry increased significantly with the increase in the fly ash content [25]. Deng et al. studied the surface properties of the particles by adding chemical additives to reduce the yield stress and slump value of the paste [26,27,28]. Xu et al. studied the rheological properties of a silica fume-modified tailings cemented filling slurry with time under a low-temperature environment and pointed out that with the prolongation of the curing time, the yield stress and viscosity increased steadily, but the decrease in the curing temperature led to a decrease in the yield stress [29]. The aforementioned research findings indicate that the current focus of research on the rheological properties of a tailings slurry primarily revolves around factors such as the cement–sand ratio, admixture, and temperature. The investigation into the impact of changes in the tailings particle gradation on rheological parameters is a relatively unexplored area, and further research is warranted.

This paper takes a lead–zinc mine in Guangdong, China as the engineering background. In order to close the tailings reservoir on the surface, the waste rock is mined underground as a building material, and the empty area generated by the mining waste rock is used to store the ultra-fine tailings, which are used to be discharged to the tailings reservoir. The permeability coefficient of ultra-fine tailings is in the order of magnitude of 10⁻⁷ cm/s, which cannot meet the requirements of non-cemented filling. By incorporating graded tailings to modify the hydraulic properties of ultra-fine tailings, it is possible to satisfy the requirements for non-cemented filling. Second, the particle size distribution of ultra-fine tailings is poor and can be improved by adding graded tailings to adjust the gradation. However, the varying proportion of graded tailings will result in alterations to the gradation of mixed tailings. The influence of the tailings gradation on the rheological parameters of a slurry should not be disregarded, as it inevitably impacts the fluidity of the filling slurry. Therefore, the research on the rheological properties and flow properties of a tailings slurry with different solid concentrations is carried out, and the impact of variations in the tailings particle size distribution on the rheological parameters and slump is examined. The correlation between the rheological parameters and slump of a tailings slurry with different mass concentrations and the gradation of tailings particles is further revealed. The research findings can offer theoretical guidance for the mine in selecting an appropriate range of particle sizes and slurry mass concentrations.

2. Materials and Methods

2.1. Materials

The tailings used in this test are mainly from a lead–zinc mine in Guangdong, China. The overflow tailings (OT) come from the underflow of a φ30 m ordinary thickener in the filling station, and the classified tailings sample (CT) comes from the classified tailings storage field. The physical properties of OT and CT are shown in

Table 1. Physical properties of materials.

Category	Particle Density (g/cm³)	Dense Density (g/cm³)	Compactness (%)	Porosity (%)	Permeability Coefficient (cm/s)
OT	3.06	1.27	42	58	3.6 × 10−7
CT	3.11	1.84	60	40	6.8 × 10−3

. The chemical compositions of the tailings were analyzed by X-ray fluorescence (XRF) spectroscopy, and the analysis results are shown in

Table 2. Chemical composition of tailings (%).

Category	CaO	SiO2	SO3	Fe2O3	Al2O3	MgO	ZnO	PbO	Other
CT	24.64	23.85	21.20	16.40	7.23	2.14	0.98	0.96	2.6
OT	20.68	26.69	18.32	10.23	16.57	2.28	1.12	0.84	3.27

. The results show that the main components of CT are CaO, SiO₂, SO₃ and Fe₂O₃, and the contents are 24.64%, 23.85%, 21.20% and 16.40%, respectively. However, the main components of OT are CaO, SiO₂, SO₃ and Al₂O₃, with contents of 20.68%, 26.69%, 18.32% and 16.57%, respectively. The comparative analysis shows that CaO, SiO₂ and SO₃ account for a large proportion of the two kinds of tailings. In CT, Fe₂O₃ accounts for 6.17 % more than OT, and Al₂O₃ accounts for 9.34% less than OT.

2.2. Mixing Tailings Aggregate Ratio and Particle Gradation Characteristics

The particle size test results of OTS and GT tailings are shown in Figure 1. The results show that the particle size of OTS is between 0.85 and 124.37 μm, of which −19 μm accounts for 70.5% and −37 μm accounts for 87.5%. The non-uniformity coefficient C_u is 7.91, and the curvature coefficient C_c is 2.64. The particle size of GTS is between 2.78 and 407.85 μm, of which −19 μm accounts for 6.50%, −37 μm accounts for 15.42% and − 74 μm accounts for 35.88%. The non-uniformity coefficient C_u is 4.77, and the curvature coefficient C_c is 1.18. In summary, the gradations of the two tailings are poor. Therefore, the mixing of the two kinds of tailings is used to improve the gradation. It exhibits excellent workability characteristics during filling operations and is highly resistant to segregation and bleeding [30].

In order to determine the ratio range of OT and GT, according to the basic physical properties of the two tailings, the two-dimensional compaction theory is used to optimize, as shown in Equation (1) [31].

$$\varphi =\{\begin{array}{l}\frac{1}{\rho }\cdot {\left(\frac{1}{{\rho }_1}+\frac{1-x}{{\rho }_2{\varphi }_2}\right)}^{-1},x<\frac{{\rho }_1{\varphi }_1}{\rho }\\ \frac{1}{\rho }\cdot {\left(\frac{1}{{\rho }_1({\varphi }_2+1-\frac{\rho }{{\rho }_1})}+\frac{1-x}{{\rho }_2{\varphi }_2}\right)}^{-1},x>\frac{{\rho }_1{\varphi }_1}{\rho }\\ \rho ={\left[\frac{x}{{\rho }_1}-\frac{1-x}{{\rho }_2}\right]}^{-1},0\le x\le 1\end{array}$$

(1)

where ρ₁ is the dense density of OT (t/m³), ρ₂ is the dense density of GT (t/m³), ρ is the dense density of mixed tailings (t/m³), ϕ₁ is the packing compactness of OT, ϕ₂ is the packing compactness of GT, ϕ is the packing compactness of mixed tailings and x is the mass percentage of OT in mixed tailings (%).

The relationship between the density of mixed tailings and the percentage of OT is shown in Figure 2. The compactness is large when the proportion of OT is less than 47%, and the compactness is the largest when the proportion of OT is 20%. The compactness test was utilized for indoor verification, as evidenced by the measured curve in Figure 2. The findings indicate a fundamental concurrence between the two.

According to the maximum density theory, the proportions of OT in this test were determined to be 8%, 16%, 23%, 31% and 39%, respectively, which were recorded as PT1, PT2, PT3, PT4 and PT5. The LMS-30 laser particle size analyzer was used to analyze the particle size, and the results are shown in Figure 3. At the same time, the characteristic values of the tailings particle size d₁₀, d₃₀, d₅₀, d₆₀, d₉₀ and d_av (average particle size) were obtained, and the non-uniformity coefficient C_u and curvature coefficient C_c of various tailings were calculated. The results are shown in

Table 3. Particle size gradation characteristic values of mixed tailings with different proportions.

Category	d10 (µm)	d30 (µm)	d50 (µm)	d60 (µm)	d90 (µm)	dav (µm)	Cu	Cc
PT1	16.6	54.07	93.77	118.81	253.62	55.20	7.16	1.48
PT2	10.36	42.89	83.41	108.86	246.24	50.40	10.51	1.63
PT3	6.43	33.24	74.38	97.47	239.88	46.20	15.16	1.76
PT4	4.47	23.58	63.1	87.31	231.57	41.40	19.53	1.42
PT5	4	17.33	50.38	74.49	220.49	36.60	18.62	1.01

. The results show that the particle size characteristic values of all kinds of tailings are different. At the same time, the C_u of all kinds of tailings is greater than 5, and the C_c is between 1 and 3.

2.3. Experimental Methods

This experiment mainly tests the slump and rheological parameters of a tailings slurry with different concentrations and reveals the correlation between the slump and rheological parameters and tailings particle gradation. Four concentrations were prepared for each type of tailing, and the mass concentrations (m_c) of the slurry were 72%, 74%, 76% and 78%, respectively.

The Brookfield R/S+ rheometer was used to determine the rheological properties. The VT-40-20 paddle rotor was equipped with a blade diameter of 20 mm and a height of 40 mm. The rheometer is equipped with a water bath temperature control system, which maintains a constant temperature of 20 °C during the experiment. During the test, the shear rate is set to 0~120 s⁻¹, the change rate is 1 s⁻¹/s, the test time is 120 s and a data point is collected per second to obtain the change curve of the shear stress and shear rate [32]. When the slurry fluidity test is carried out, the slump cylinder is used to characterize the slump [33]. The flow chart of the study is shown in Figure 4.

3. Results and Discussion

3.1. Experimental Results

Research has indicated that, in fluids containing a high concentration of solid particles, such as a tailings slurry, the fine particles have an affinity for each other and tend to aggregate into flocs. With the increase in the solid content, flocs become interconnected, forming a loosely structured network known as the floc network structure. The floc network structure has a certain shear strength, which makes the slurry have a certain initial strength, which is called the yield stress. Here, the Bingham model is used to describe its rheological properties [34], as shown in Equation (2):

$${\tau }_w={\tau }_0+\mu \stackrel{·}{\gamma }$$

(2)

where τ_w is the shear stress (Pa), τ₀ is the yield stress (Pa), μ is the plastic viscosity (Pa·s) and  is the shear rate (s⁻¹).

The test results of the slump and rheological parameters of the tailings slurry with different mass concentrations are shown in

Table 4. Test results of the rheological parameters and slump of the tailings slurry at different mass concentrations.

Category	Mass Concentrations/%	τ0/Pa	µ/Pa·s	Slump/cm
PT1	72	7.240	0.15	29.6
	74	14.32	0.27	29.0
	76	56.30	0.29	28.5
	78	103.56	0.38	27.8
PT2	72	9.89	0.19	28.9
	74	26.75	0.23	28.4
	76	63.84	0.33	27.9
	78	144.09	0.46	26.8
PT3	72	12.42	0.21	28.4
	74	28.92	0.30	27.9
	76	73.27	0.45	27.4
	78	160.74	0.51	26.5
PT4	72	16.62	0.35	27.8
	74	33.50	0.43	27.3
	76	77.13	0.52	26.8
	78	167.86	0.63	26.0
PT5	72	31.49	0.37	27.2
	74	58.77	0.44	26.7
	76	106.18	0.56	26.2
	78	182.51	0.65	25.4

.

3.2. Analysis of the Rheological Properties of the Tailings Slurry

As shown in Table 4, the change in the tailings particle gradation and mass concentration has a significant effect on the rheological parameters of the slurry. The curve of the shear stress of the tailings slurry with the shear rate is shown in Figure 5. When the mass concentration is 76% and 78%, the shear stress of the PT1 and PT3 tailings slurry increases rapidly with the increase in the shear rate, that is, significant stress overshoot occurs, and the static yield stress of the PT1 tailings slurry is significantly lower than that of the PT3 tailings slurry. The reason is that, with the increase in the the proportion of OT, the smaller the particle size of the tailings, the denser the floc network structure between the particles. This results in an increase in the static yield stress, as a higher shear stress is required to disrupt the internal structure of the slurry [35]. However, when the slurry concentration is 72~74%, there is no obvious stress overshoot phenomenon, indicating that the change in mass concentration has a more significant effect on the rheological properties of the slurry than the tailings particle gradation.

3.3. The Variation Characteristics of the Tailings Slurry Slump

According to the findings in Table 4, it is evident that as the mass concentration increases, there is a noticeable decrease in the slump when keeping the tailings particle gradation constant. Therefore, the increase in the mass concentration will have an adverse effect on the flow performance of the slurry. In order to quantify the relationship between the mass concentration and slump, the variation in the slump with the mass concentration of different types of tailings slurries is drawn, as shown in Figure 6. The results show that the slump of the tailings slurry exhibits a quadratic function with the increase in the mass concentration and shows a decreasing trend, The relative error between the fitting results and the measured values is between −9.07% and 7.02%, and the correlation coefficient of the fitting results is R² ≥ 0.957. For different types of tailings, the mass concentration of the slurry increased from 72% to 78%, and the slump decreased by 6.08%, 7.27%, 8.10%, 8.99% and 9.19%, respectively. With the decrease in the tailings particle size, the decrease in the slurry slump also gradually increases, indicating that the sensitivity of the tailings slurry slump to the mass concentration increases with the decrease in the tailings particle size. The increase in the slurry mass concentration means that the mixing water decreases continuously, which makes the spacing between the particles gradually decrease, enhances the cohesion between the particles and then reduces its flow performance. In addition, when the mass concentration is fixed, the slump index of the PT1 tailings slurry is the highest, followed by PT2, PT3 and PT4, and the worst is the PT5 tailings slurry. The reason is that as the fine particles of the tailings slurry gradually increase, the lubrication effect of the fine particles is weakened, resulting in the formation of a large number of flocculent network structures between the fine particles, which increases the flow resistance of the tailings particles and further deteriorates its flow performance [36].

3.4. Variation Characteristics of the Rheological Parameters of the Tailings Slurry

According to Table 4, the variation in the rheological parameters of different types of tailings slurries with mass concentrations is drawn and shown in Figure 7. The results show that the change in the mass concentration has a significant effect on the yield stress of the slurry. With the increase in the mass concentration, the yield stress basically follows the quadratic function increasing law, while the plastic viscosity shows a linear growth law. The relative error between the fitting results and the measured values is between −9.6% and 10.4%, and the correlation coefficient of the fitting results is R² > 0.97, indicating that the increase in the concentration will significantly improve the rheological parameters of the slurry. From Figure 7a, it can be seen that when the mass concentration increases from 72% to 78%, the yield stress of the PT1, PT2, PT3, PT4 and PT5 tailings slurries increases by 13.31 times, 13.56 times, 11.94 times, 9.09 times and 4.79 times, respectively. It can be seen that the increase in the yield stress has a significant correlation with the type of tailings. The specific performance is that the thicker the tailings particles, the greater the increase in the yield stress, and the sensitivity of the yield stress to the mass concentration decreases with the increase in the fine particles of the tailings slurry. It can be seen from Figure 7b that when the mass concentration increases from 72% to 78%, the plastic viscosity of the PT1, PT2, PT3, PT4 and PT5 tailings slurries increases by 1.53 times, 1.42 times, 1.43 times, 0.81 times and 0.71 times, respectively. It can be seen that the increase in the plastic viscosity also has a significant correlation with the type of tailings. The thicker the tailings particles are, the greater the increase in the plastic viscosity is. The sensitivity of the plastic viscosity to the mass concentration also decreases with the increase in the fine particles of the tailings slurry. When the mass concentration is fixed, the yield stress of the PT1 tailings slurry is the smallest, followed by PT2, PT3 and PT4, and the highest is the PT5 tailings slurry. The reason is that, with the decrease in the particle size of the tailings, the fine particles in the tailings slurry gradually increase, which weakens the lubrication effect of the fine particles, resulting in the formation of a large number of flocculent network structures between the fine particles, thereby increasing the yield stress of the slurry.

4. The Correlation between the Rheological Parameters and Slump and Tailings Particle Gradation

4.1. Relationship between the Rheological Parameters and Slump of Different Types of Tailings Slurries

Figure 8 shows the relationship between the rheological parameters and slump of different types of tailings slurries. From Figure 8a, it can be seen that the yield stress of different types of tailings slurries basically follows a quadratic function with the increase in the slump, showing a decreasing trend, and the fitting regression coefficients are all greater than 0.93. The relative errors between the fitting results and the measured values are between −10.23% and 9.84%, so the regression model can meet the engineering application of the mine site. The relationship between the yield stress and slump for different types of tailings slurries is shown in Equation (3), and the fitting equation is shown in

Table 5. Model fitting coefficient of yield stress–slump of the tailings slurry.

Category	a	b	c	R2
PT1	22.533	−1349.290	20,200.913	0.937
PT2	8.755	−554.168	8693.821	0.981
PT3	30.823	−1770.437	25,432.228	0.999
PT4	40.812	2279.389	31,842.568	0.999
PT5	15.206	−884.882	12,849.213	0.994

.

$${\tau }_0=a{s}^2+bs+c$$

(3)

where τ₀ is the yield stress of the slurry (Pa), s is the slump of the slurry (cm) and the regression coefficients of the a, b and c models are related to parameters such as the tailings particle gradation and slurry concentration.

It can be seen in Figure 7b that the plastic viscosity of different types of tailings slurries basically follows the linear growth law with the increase in the slump, indicating that the linear function can quantitatively characterize the relationship between the slurry plastic viscosity and slump. The relationship between the plastic viscosity and slump of different types of tailings slurries is shown in Equation (4), and the relevant parameters are shown in

Table 6. Model fitting coefficient of plastic viscosity–slump of the tailings slurry.

Category	a1	b1	R2
PT1	3.745	−0.121	0.925
PT2	4.028	−0.133	0.978
PT3	4.836	−0.162	0.878
PT4	4.706	−0.157	0.995
PT5	4.439	−0.149	0.943

.

$$\mu =a_{1}s+b_1$$

(4)

where $\mu$ is the plastic viscosity of the slurry (Pa·s), s is the slump of the slurry (cm) and a₁ and b₁ are the regression coefficients of the model, which are related to parameters such as the tailings particle gradation and slurry concentration.

4.2. Correlation Analysis of the Slump and Particle Gradation

According to the previous analysis, when the mass concentration is fixed, there are obvious differences in the slump of different types of tailings slurries. This indicates that the change in the tailings particle gradation can have a significant impact on the slump. Therefore, it is necessary to further explore the correlation between the tailings particle gradation and slump under different mass concentrations. In order to explore the correlation between the slump s of the tailings slurry and the particle gradation parameter x, the least square method is used for fitting [37]:

$$s=a_{2}x+b_2$$

(5)

According to the fitting results, the correlation coefficient R² between s and x is obtained. When 0.8 < R² ≤ 1, the slump s is extremely correlated with the particle gradation parameter x. When 0.6 < R² ≤ 0.8, the slump s is strongly related to the particle gradation parameter x. When 0.4 < R² ≤ 0.6, the slump s is moderately correlated with the particle gradation parameter x. When R² ≤ 0.4, the slump s is not or weakly related to the particle size distribution parameter x.

Combined with the data in Table 4, the least square method is calculated according to the correlation equation, and the fitting results of various tailings slurries are obtained. Due to the limited space, this analysis only listed the fitting results of the mass concentrations of 72% and 74%, as shown in

Table 7. Correlation results between the slurry slump and tailing particle gradation.

Mass Concentration/%	Fitting Results	a2	b2	R2
72	s = a2 × d10 + b2	0.168	26.792	0.853
	s = a2 × d30 + b2	0.063	26.221	0.989
	s = a2 × d50 + b2	0.055	24.372	0.993
	s = a2 × d60 + b2	0.053	23.178	0.993
	s = a2 × d90 + b2	0.072	11.198	0.983
	s = a2 × dav + b2	0.128	22.510	0.998
76	s = a2 × d10 + b2	0.161	26.015	0.828
	s = a2 × d30 + b2	0.060	25.278	0.984
	s = a2 × d50 + b2	0.053	23.488	0.997
	s = a2 × d60 + b2	0.051	22.330	0.997
	s = a2 × d90 + b2	0.069	10.727	0.989
	s = a2 × dav + b2	0.123	21.686	0.999

. At the same time, the variation in the fitting correlation coefficient R² with the characteristic particle size value is obtained, as shown in Figure 9. It can be seen in Table 7 that the correlation coefficient between the slump of the tailings slurry and the characteristic particle size value exceeds 0.80 at different mass concentrations, indicating that the slump of the tailings slurry is extremely correlated with the particle size characteristics. When the mass concentration is 72%, the correlation coefficient between the slump and d₁₀ is 0.853, and the two are extremely correlated. With the increase in the characteristic particle size, the correlation coefficient shows an increasing trend, indicating that the correlation between the two increases with the increase in the characteristic particle size. When the mass concentration is 78%, the correlation coefficient between the slump and d₁₀ is 0.828, and the two are also extremely correlated. However, with the increase in the characteristic particle size, the correlation coefficient shows a trend of increasing first, then decreasing and then increasing, indicating that the correlation degree between the slump and the characteristic particle size is also related to the mass concentration range of the slurry. It can be seen in Figure 9 that when the mass concentration is fixed, the correlation coefficient increases with the increase in the characteristic particle size, indicating that the correlation between the slump and the characteristic particle size is also gradually enhanced. However, the slump of the tailings slurry with a mass concentration of 78% has the lowest correlation coefficient with d₃₀, d₅₀, d₆₀, d₉₀ and d_av, indicating that the increase in concentration will weaken the correlation between the slump of the tailings slurry and the characteristic particle size.

4.3. Correlation Analysis of Rheological Parameters and Particle Size Distribution

When the mass concentration is fixed, there are obvious differences in the rheological parameters of different types of tailings slurries, indicating that the change in the tailings particle gradation can have a significant impact on the rheological parameters. Therefore, it is necessary to further explore the correlation between the tailings particle gradation and rheological parameters under different mass concentrations so as to provide theoretical guidance for the mine to select a reasonable particle size range. In order to explore the correlation between the rheological parameter y of the tailings slurry and the particle gradation parameter x, the least square method is also used for fitting, and the evaluation criteria are the same as the above [38,39].

$$y=a_{3}x+b_3$$

(6)

Combined with the test data in Table 4, the least square method is calculated according to the correlation equation, and the fitting results under different types of tailings slurries are obtained. Limited to the space, this analysis only lists the fitting results of tailings slurries with mass concentrations of 72% and 74%, as shown in

Table 8. Correlation results between the slurry yield stress and tailing particle gradation.

Mass Concentration/%	Fitting Results	a3	b3	R2
72	y = a3 × d10 + b3	−1.343	26.776	0.388
	y = a3 × d30 + b3	−0.567	34.899	0.680
	y = a3 × d50 + b3	−0.572	54.023	0.832
	y = a3 × d60 + b3	−0.509	65.089	0.814
	y = a3 × d90 + b3	−0.707	183.960	0.872
	y = a3 × dav + b3	−1.202	70.787	0.791
76	y = a3 × d10 + b3	−1.129	114.788	0.741
	y = a3 × d30 + b3	−1.035	151.714	0.864
	y = a3 × d50 + b3	−1.001	173.684	0.851
	y = a3 × d60 + b3	−1.382	405.626	0.895
	y = a3 × d90 + b3	−2.372	185.162	0.833
	y = a3 × dav + b3	−1.129	114.788	0.741

and

Table 9. Correlation results between the slurry plastic viscosity and tailing particle gradation.

Mass Concentration/%	Fitting Results	a3	b3	R2
72	y = a3 × d10 + b3	−1.343	26.776	0.640
	y = a3 × d30 + b3	−0.567	34.899	0.866
	y = a3 × d50 + b3	−0.572	54.023	0.890
	y = a3 × d60 + b3	−0.509	65.089	0.871
	y = a3 × d90 + b3	−0.707	183.960	0.881
	y = a3 × dav + b3	−1.202	70.787	0.887
76	y = a3 × d10 + b3	−1.129	114.788	0.844
	y = a3 × d30 + b3	−1.035	151.714	0.964
	y = a3 × d50 + b3	−1.001	173.684	0.932
	y = a3 × d60 + b3	−1.382	405.626	0.951
	y = a3 × d90 + b3	−2.372	185.162	0.909
	y = a3 × dav + b3	−1.129	114.788	0.948

. It can be seen in Table 8 that when the mass concentration is 72%, the correlation coefficients of the yield stress with d₁₀ and d₃₀ are 0.388 and 0.680, respectively, indicating that the yield stress is irrelevant or weakly correlated with d₁₀ but strongly correlated with d₃₀. However, with the increase in the characteristic particle size, the correlation coefficient between the yield stress and particle gradation increases, indicating that the increase in the characteristic particle size will enhance the correlation between the yield stress and particle gradation. When the mass concentration is 76%, the correlation coefficient between the yield stress and d₁₀ is 0.741, indicating that there is a strong correlation between them. With the increase in the characteristic particle size, the correlation coefficient between the yield stress and gradation parameters also increases gradually, indicating that the correlation is also enhanced. It can be seen in Table 9 that when the mass concentration is 72%, the correlation coefficient between the plastic viscosity and d₁₀ is 0.640, indicating that the two are strongly correlated. With the increase in the characteristic particle size, the correlation coefficient between the plastic viscosity and gradation parameters also increases gradually, indicating that the correlation is also enhanced. When the mass concentration is 76%, the correlation coefficient between the plastic viscosity and the grading parameters exceeds 0.80, indicating that there is a very strong correlation between the two, and the correlation coefficient is higher than the correlation coefficient between the plastic viscosity and the characteristic particle size of the slurry with a mass concentration of 72%. The increase in the mass concentration will also enhance the correlation between the plastic viscosity and characteristic particle size.

The variation trend of the correlation coefficient R² of the yield stress and plastic viscosity of tailings slurry with the gradation parameters of tailings particles at different mass concentrations is shown in Figure 10. It can be seen from Figure 10a that when the mass concentration is 72~76%, the correlation coefficient increases most obviously at d₁₀~d₅₀, indicating that when the particle size characteristics increase from d₁₀ to d₅₀, the correlation between the yield stress and particle gradation parameters increases significantly, indicating that the change in the particle size in this range has a significant effect on the yield stress of the slurry. When the concentration increases to 78%, the correlation coefficient shows a downward trend at d₁₀~d₅₀, indicating that the significant increase in the concentration can affect the correlation between the gradation parameters of the tailings particles and the yield stress. This indicates that the correlation between the yield stress and the gradation parameters of tailings particles has a significant correlation with the mass concentration. It can be seen in Figure 10b that the correlation coefficient between the plastic viscosity and gradation parameters increases first and then stabilizes with the increase in the characteristic particle size at different mass concentrations, and the correlation coefficient increases most significantly at d₁₀~d₅₀, indicating that the change in the particle size in this range can have a significant impact on the plastic viscosity of the slurry, and the difference in the mass concentration will also lead to a significant difference in the correlation coefficient, indicating that the correlation between the plastic viscosity and gradation parameters of tailings particles also has a certain correlation with the mass concentration.

5. Tailings Ratio Optimization

A lead–zinc mine in Guangdong is filled by gravity flow transportation. The rheological parameters of the slurry are the key to determining the resistance of pipeline transportation. When the gravitational potential energy of the slurry in the transportation process is greater than the total resistance loss of the pipeline, the tailings slurry can be transported to the goaf. However, there are significant differences in the rheological parameters of different types of tailings at different mass concentrations. It is necessary to calculate the pipeline resistance loss in the transportation process of the mixed tailings slurry with different types and different mass concentrations and compare it with the gravitational potential energy in the transportation process of the slurry so as to optimize the reasonable proportioning parameters. The calculation of the pipe flow resistance of the mixed tailings is shown in Equation (7). Through Equation (8), the total resistance loss of the pipeline can be calculated according to the pipeline transportation distance. The gravitational potential energy in the transport process of the slurry is shown in Equation (9) [40,41].

$$i_m=\frac{16{\tau }_0}{3D}+\frac{32}{D^2}\mu$$

(7)

where i_m is the pipe flow resistance (Pa/m), D is the inner diameter of the pipe (m) and v is the flow rate of the pipeline (m/s).

$$h_m=i_m{L}_m$$

(8)

where h_m is the total resistance of the pipeline (Pa) and L_m is the total length of the pipeline (m).

The gravitational potential energy in the process of slurry transportation can be calculated by the following expression:

$$P={\rho }_{m}gH$$

(9)

where ρ_m is the slurry density (kg/m³), H is the vertical pipe height (m) and g is the acceleration of gravity (9.8 m/s²).

Taking the filling of a −600 m middle goaf in a lead–zinc mine in Guangdong, China as a case study, the gravitational potential energy and total resistance in the process of slurry transportation were calculated. The inner diameter of the mine filling pipe is 0.1 m, and the flow rate of the filling slurry is designed to be 2.5 m/s. The vertical pipeline height corresponding to a stope in the middle section is 628 m, and the total length of the pipeline is 2015 m. The transportation resistance of various kinds of tailings slurries can be calculated by Equations (7) and (8). According to Equation (9), the gravitational potential energy of a slurry in the conveying process can be calculated. The relevant calculation results are shown in

Table 10. Calculation results of the total resistance loss and gravitational potential energy of various tailings transportation.

Category	Mass Concentration/%	τ0/Pa	u/Pa·s	hm/MPa	P/MPa
PT1	72	7.240	0.15	3.20	10.17
	74	14.32	0.27	5.89	9.89
	76	56.30	0.29	10.72	9.62
	78	103.56	0.38	17.25	9.37
PT2	72	9.89	0.19	4.13	10.17
	74	26.75	0.23	6.58	9.88
	76	63.84	0.33	12.18	9.62
	78	144.09	0.46	22.90	9.36
PT3	72	12.42	0.21	4.72	10.16
	74	28.92	0.30	7.94	9.88
	76	73.27	0.45	15.13	9.61
	78	160.74	0.51	25.49	9.36
PT4	72	16.62	0.35	7.43	10.16
	74	33.50	0.43	10.53	9.88
	76	77.13	0.52	16.67	9.61
	78	167.86	0.63	28.19	9.35
PT5	72	31.49	0.37	9.35	10.15
	74	58.77	0.44	13.41	9.87
	76	106.18	0.56	20.44	9.60
	78	182.51	0.65	30.09	9.35

. When the mass concentration is 72%, the mixed tailings filling slurry of PT1~PT5 types can meet the demand of gravity transportation, and the amount of overflow tailings (OT) can reach 39%. When the mass concentration is 74%, the mixed tailings filling slurry of PT1~PT3 types can meet the demand of gravity transportation, while the mixed tailings slurry of PT4 and PT5 types cannot meet the demand of gravity transportation, and the mixing amount of overflow tailings (OT) can reach 23%. When the mass concentration reaches 76~78%, the mixed tailings filling slurry of PT1~PT5 types cannot meet the requirements of gravity transportation, so the mass concentration of a mixed tailings filling slurry should be lower than 76%. In summary, when the mass concentration of the mine is designed to be 72%, the incorporation of overflow tailings (OT) can reach 8~39%, and when the mass concentration is designed to be 74%, the incorporation of overflow tailings (OT) can reach 8~23%, and the maximum mass concentration of the slurry should be less than 76%.

6. Conclusions

The experimental study on the rheological properties and flow properties of mixed tailings filling slurries was carried out. The influence of the tailings particle gradation and mass concentration on the rheological and flow properties was analyzed. The mathematical model of the rheological parameters and slump was constructed, and the correlation between the rheological parameters, slump, and tailings particle gradation parameters was discussed. Finally, the ratio parameters of the mixed tailings filling slurry were optimized, and the following conclusions were obtained:

(1)

The slump of the tailings slurry shows a quadratic function decreasing trend with the increase in the mass concentration, and the decrease in the slump increases with the decrease in the particle size. The sensitivity of the tailings slurry slump to the mass concentration increases with the decrease in the tailings particle size.

(2)

With the increase in the mass concentration, the yield stress of the tailings slurry basically follows the law of quadratic function increasing, while the plastic viscosity shows a linear growth law. The thicker the tailings particles are, the greater the increase in the yield stress and plastic viscosity is. The sensitivity of the yield stress and plastic viscosity to the mass concentration decreases with the increase in the fine particles of the tailings slurry.

(3)

The yield stress of different types of tailings slurries basically follows the trend of a quadratic function decreasing with the increase in the slump, while the plastic viscosity basically follows the linear growth law with the increase in the slump.

(4)

At different mass concentrations, the slump of the tailings slurry is extremely correlated with the characteristic particle size of the particles, and the degree of correlation between the slump and the characteristic particle size also has a certain relationship with the mass concentration range of the slurry. The specific performance is as follows: when the mass concentration is low, the correlation between the slump and the aggregate size grading parameters gradually increases with the increase in the characteristic particle size, but when the concentration is high, the increase in the mass concentration will weaken the correlation between the slump of the tailings slurry and the characteristic particle size.

(5)

When the mass concentration is 72~76%, the correlation coefficient increases most obviously at d₁₀~d₅₀, and the increase in the particle size characteristic value will enhance the correlation between the yield stress and particle gradation. The correlation coefficient between the plastic viscosity and gradation parameters increases first and then tends to be stable with the increase in the characteristic particle size, and the correlation coefficient increases most significantly at d₁₀~d₅₀, indicating that the change in the particle size in this range can have a significant impact on the plastic viscosity of the slurry.

(6)

When the mass concentration of the mine is designed to be 72%, the amount of overflow tailings (OT) can reach 8~39%, and when the mass concentration is designed to be 74%, the amount of overflow tailings (OT) can reach 8~23%, and the maximum mass concentration of the slurry should be less than 76%.

Through the research of this paper, the correlation between the characteristic value of the tailings particle size and the rheological parameters is quantified, which provides the basis for the optimization of particle size distribution in the process of a filling operation and provides technical support for saving pumping costs.