Complexity
Volume 2019 (2019), Article ID 3591628, 13 pages
https://doi.org/10.1155/2019/3591628

Research Article

Permeability Prediction of Iron Tailings Including Degree of Compaction and Structure

Deqing Gan, Xi Yang, and Yunpeng Zhang

North China University of Science and Technology, Hebei Mining Key Laboratory of Development and Safety Technology, Tangshan, Hebei 063000, China

Correspondence should be addressed to Xi Yang; ncst-lzy@ncst.edu.cn

Received 18 June 2019; Accepted 12 August 2019; Published 25 September 2019

Academic Editor: Dimitri Volchenkov

Copyright © 2019 Deqing Gan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The stability of iron tailings dam is affected by the permeability of tailings. Considering the influence of it, it is necessary to analyze the permeability of tailings so as to prevent the recurrence of Brazilian iron tailings dam accidents. Nevertheless, the results of iron tailings permeability from some prediction equations (Terzaghi equation, Hazen equation, and Kozeny equation) cannot be accurate. Iron tailings are various as they can be divided into three categories: (1) silt content is less than 40%; (2) silt content is more than 40%, while clay content is less than 15%; and (3) clay content is more than 15% and less than 30%. Correspondingly, three equations are proposed to calculate the disturbed and iron undisturbed tailings permeability for the three types. And more accurate results come from it. The water-flow paths of the iron tailings are blocked after compaction, and the critical pressure of iron tailings blockage is 200 kPa. Although the porosity is large, some of the pores are isolated from each other when the pressure is larger than 200 kPa. However, porosity becomes too large for permeability calculation after compaction and the calculated permeability gets larger as well (equations (24)–(26)). Correcting the permeability calculation equations is an absolute must. The calculated permeability by the revised equations becomes more accurate (equations (27)–(29)). In fact, the granulometric characteristics necessarily play a vital role in the evolution of the pore interconnections by blocking the water-flow paths and modifying the morphological parameters. More research studies are required to be done in the future.

1. Introduction

Soil permeability is the ability to allow water to flow under a hydraulic head. It is one of the most significant geotechnical properties of soil and gets involved in the design of retaining structures and earthen dams. In addition, the permeability of tailings has an impact on the stability of tailings dam [1, 2]. But permeability has not yet been classified as a parameter for design with several constraints related to its measurement [3, 4]. Many permeability measurements are very tough, time-consuming, and expensive. It is very unfavorable for a wide range of measuring the permeability coefficients. Therefore, many analytical equations have been proposed to predict the permeability of fine-grained soil.

Beven and Germann found that water flowing in soils occurs mainly in macropores. Thus, a capillary model has been proposed to estimate the soil permeability [5]. This model is widely applied for predicting the permeability coefficients. The porous medium consists of straight parallel channels with a cylindrical shape in the model. The permeability coefficient (K) is predicted by the following equation:

where p = porosity and d =  is the mean diameter of channels.

The approximation of the straight channel is corrected by the curvature (τ), and the channel is assumed to be oriented in three spatial directions, and the porous medium is considered to be isotropic and homogeneous. The curvature (τ) makes the prediction of permeability coefficient more accurate. According to Saffman [6], equation (1) becomes

The porous medium consists of tortuous cylindrical channels. The permeability coefficient (K) is expressed as a quadratic function of the characteristic size of the channels. However, for the Carman–Kozeny model, the permeability coefficient (K) is expressed as a function of the specific surface area (As). Both have their own scope of application. The Carman–Kozeny model is as follows [7]:

where k = shape factor.

After determining the relevant parameters, the Kozeny equation is as follows [8]:

The Terzaghi equation and Hazen equation are also applied for predicting the permeability coefficient. However, the permeability coefficient (K) is expressed as a quadratic function of the particle size in the Hazen equation. In addition, the permeability coefficient (K) is expressed as a quadratic function of the particle size and void ratio in the Terzaghi equation.

The Terzaghi equation is as follows [8]:

The Hazen equation is as follows [9]:

where K is the permeability coefficient of the sample soil at 20°C; d₉ and d₁₀ are, respectively, the sample soil particle diameter (cm) corresponding to the cumulative content of 9% and 10%; dθ = d₂₀ (cm); e = void ratio; and n = porosity.

As reported by Schwartz et al., the permeability coefficient (K) of a sediment is generally controlled by many factors such as pore dimensions, topology, or connectedness. Thus, the following equation is proposed to predict the permeability coefficient (K) of a sediment [10–15]:

The permeability coefficient (K) is expressed as a quadratic function of the effective pore radius (reff). reff cannot be regarded as an actual geometric measure but as a characteristic length scale [16]. By introducing the formation resistivity factor (F) to correct the approximation of channels, equation (7) makes the prediction of permeability coefficient more accurate. The formation resistivity factor (F) combines information about porosity (ϕ), connectedness (χ), and electric tortuosity (τ):

As reported by Walker and Glover, the topology of the pore space is described by the packing constant (a) [17]. The sediment permeability coefficient is then estimated with the RGPZ model [15]. The RGPZ model is as follows:

In order to simplify the calculation process, many existing empirical equations replace these structural variables (a, m, and F) with an empirically defined coefficient [18, 19]. Thus, the RGPZ model can be written as equation (10). It only applies to certain soils:

where a = sediment packing constant, unitless; F = formation resistivity factor, unitless; deff = effective grain diameter, m; reff = effective pore radius, m; and K = permeability, m².

These existed models are mainly based on empirical methods and Darcy’s law. Factors considered by these models may not apply to tailings. More factors need to be taken into account for iron tailings. Tailings are different from other soils. It contains a lot of fine particles, such as silt particles and clay particles. The permeability coefficient of tailings varies greatly because of the change in fine particle content. Furthermore, the structure of tailings varies from other soils due to the discharge method of tailings. The bottom tailings are continuously compressed with the increasing height of the tailings dam. Structure and degree of compaction are important factors affecting the permeability of tailings. But these factors have not been considered in the above equations. For avoiding the recurrence of Brazilian tailings dam accidents, it is imperative to analyze the permeability of tailings. In this paper, the permeability properties of iron tailings were analyzed by fine particle content, structure, and degree of compaction. A series of new equations with improved accuracy for calculating the permeability coefficient of iron tailings were proposed, which plays a major role in analyzing the stability of tailings dams.

2. Materials and Experimental Setup

2.1. Preparation of Experimental Samples

The iron tailings samples (Figure 1) used in the test are taken from the Chenkeng tailings reservoir (Figure 1) in Fujian Province, China. These samples maintain the original internal structure of the tailings. First, we apply Vaseline to the inner wall of the ring cutter which prevents water from escaping from the wall of the ring cutter. The diameter of the ring cutter is 61.8 mm, and the height is 40 mm. Then, four ring cutters are loaded into a sampler (Figure 1). The samplers are used to take the iron tailings samples at different distances from the tailings dam. The sampling depth of the iron tailings samples is the same. The sampler must be sealed immediately to keep the water from draining after sampling. The dry density of the samples is about 2.10 g/cm³ [20].

Figure 1: The sampler and sampling area.

2.2. Experimental Setup

Experiments were conducted by a permeameter that consists of a water outlet, a water inlet, an air outlet, two switches, a bottom cover, a top cover, a pressure cap, and three screws, as shown in Figure 2.

Figure 2: Permeameter.

The schematic of the experimental setup is shown in Figure 3. A steel tape is affixed vertically to a wall for recording the water head height. Then, a glass tube with 10 mm diameter and 1.5 m length was vertically affixed to the steel tape for generating water head pressure. A hose is bestowed to connect the lower end of the tube with the permeameter inlet. The height of the hose is the same as the height of the permeameter inlet. Then, fill the tube with water. The height of the water in the tube reaches the initial water head height. The water flows from the upright tube into the permeameter through the inlet, and then, it passes through the experimental samples from the bottom to the top before running out from the outlet. The accuracy of the test will be affected by the bubbles in the permeameter and tube. Thus, they have to be completely removed by injecting tap water and shaking the tube before starting a test.

Figure 3: Schematic plot of the experimental setup.

Based on Darcy’s law, the permeability coefficient of the tailings can be calculated using the following equation in the experiment:

where L = the height of the sample (cm); a = the cross-sectional area of the tube (cm²); t₁ and t₂ are the start and end time which the water inside the tube falls from H₁ to H₂ (s); H₁ = the initial water head height, H₂ = the final water head height (cm); η₂₀ = the dynamic viscosity of water at 20°C; and ηT = the dynamic viscosity of water at T°C (kPa) [20].

First, the initial water head height (H₁) and time (t₁) should be recorded. Then, we open the water inlet switch (Figure 2) and record the final water head height (H₂) and corresponding time (t₂). The above process is repeated 4 times. Finally, based on equation (11), the permeability coefficient of the undisturbed iron tailings is calculated. The average value is used as the permeability coefficient of this tailings sample [20].

After a permeability test, a compaction test is performed by compaction device that consists of a displacement monitor, two dowel bars, and some weights as shown in Figure 4. We can apply different pressures to the tailings sample by adding the weights. After 24 hours, the compaction test is completed. When the displacement and corresponding pressure have been recorded, another permeability test is performed. The effect of compaction on the permeability of the tailings can be figured out by compaction tests.

Figure 4: Compaction device.

Since the tests of permeability and compaction of the undisturbed iron tailings have been completed, each undisturbed iron tailings sample was dried and made into a disturbed sample with the same dry density as the undisturbed iron tailings sample. The disturbed tailings are uniform while the undisturbed tailings are layered. The test of the disturbed iron tailings is then performed, which is identical to the undisturbed ones. The disturbed iron tailings have no deposition structure and are uniform. The effect of the structure on the permeability of the tailings can be analyzed by comparing the data of the disturbed tailings with the undisturbed one.

A total of three series of tests were conducted. First, 12 groups (1-12 series) of iron tailings permeability tests were performed to figure out the influence of fine particle content on permeability coefficients. Second, 5 groups (2-5 series) of iron tailings permeability tests were performed to figure out the difference of permeability coefficients between the undisturbed tailings and disturbed tailings. Third, 13 groups (3-13 series) of iron tailings permeability and compaction tests were performed to figure out the permeability coefficients of compressed tailings.

3. Test Results

3.1. The Influence of Fine Particle Content on Permeability Coefficients

12 groups of iron tailings permeability tests were performed. The gradation curves are shown in Figure 5.

Figure 5: Gradation curves of iron tailings.

The influence of silt content on the permeability of iron tailings has been shown in Figure 6(a). This figure shows that the permeability coefficients are decreasing with the increase in the silt content at first. The reason behind this decreasing trend is that the void ratio decreases as the clay content increases. But the permeability coefficients increase slightly, when the silt content exceeds 40%. The reason behind this increasing trend is that the void ratio increases when the silt content exceeds 40% [21]. Then, the permeability coefficients continue to decrease because of the increase in clay content.

Figure 6: Permeability coefficient curves: variation of permeability coefficients with (a) silt content and (b) clay content.

The influence of clay content on the permeability of iron tailings has been shown in Figure 6(b). This figure shows that the permeability coefficients are increasing with the raise of the clay content at first. The reason behind this increasing trend is that the void ratio increases when the silt content exceeds 40% or the clay content is less than 15%. Although the void ratio is increased, the effective void ratio is decreased. Therefore, the permeability coefficients decrease when the clay content exceeds 15%.

Tailings contain a wide range of particle sizes, which is different from other soils. Different permeability occurs in different particle size ranges and content. Therefore, it is necessary to classify tailings in order to make a better analysis of their permeability.

3.2. Comparison of Permeability Coefficients between Undisturbed Tailings and Disturbed Tailings

5 groups of iron tailings permeability tests were performed. The gradation curves are shown in Figure 7.

Figure 7: Gradation curves of iron tailings.

The structure of tailings is different from other soils because of the discharge method of tailings. The influence of structure on the permeability of iron tailings has been shown in Figure 8. The permeability coefficients of the disturbed tailings are larger than those of the undisturbed ones because of sedimentary structure. The distributed tailings are uniform, and the coarse and fine particles of the undisturbed tailings are distributed in different layers. Therefore, the permeability coefficients of the undisturbed tailings are more affected by fine particles. Its permeability coefficients are smaller.

Figure 8: Permeability coefficient of the disturbed and undisturbed tailings.

3.3. The Permeability Coefficients of Compressed Tailings

13 groups of iron tailings permeability and compaction tests were performed. The gradation curves are shown in Figure 9. The iron tailings are subjected to different pressures at different depths. Therefore, each permeability test contains 8 pressure levels (0 kPa, 50 kPa, 100 kPa, 200 kPa, 400 kPa, 800 kPa, 1600 kPa, and 3200 kPa) based on the depth of the iron tailings. In total, 104 permeability tests under different pressure conditions were performed, as shown in Figure 10.

Figure 9: Gradation curves of iron tailings.

Figure 10: Variation of permeability coefficients with pressure.

The influence of pressure on the permeability of iron tailings has been shown in Figure 10. This figure shows that the permeability coefficients are decreasing with the increasing pressure. The permeability coefficients begin to slowly decrease when the pressure exceeds 800 kPa. The evolution of the permeability is becoming less significant with the low degree of compaction. The permeability channel will be blocked when the degree of compaction intensified [22]. The bottom tailings are continuously compressed when the height of the tailings dam increases. The void ratio cannot be effectively used to calculate the permeability coefficients on condition that the permeability channel blocked. Therefore, it is necessary to take pressure into consideration so as to accurately calculate the permeability coefficients in different degrees of compaction.

4. Discussion

4.1. Comparison between Experimental Permeability Coefficients and Those Provided by Permeability Soil Models

Three equations among all approaches discussed in the Introduction section were selected—Terzaghi equation, Hazen equation, and Kozeny equation. The permeability coefficients estimated from the three previously selected models are given in Figures 11–13.

Figure 11: Crossplots of the calculated permeability by equation (5) and the measured permeability.

Figure 12: Crossplots of the calculated permeability by equation (6) and the measured permeability.

Figure 13: Crossplots of the calculated permeability by equation (4) and the measured permeability.

All the undisturbed tailings samples were calculated by equations (5) and (6) in Figures 11 and 12. All calculated permeability coefficients are less than the measured permeability. Only particle size (d₁₀) and void ratio have been considered in equations (5) and (6). However, the tailings have a larger particle size range. The particle size and void ratio used to calculate the permeability coefficients of tailings in different particle size ranges should be varying. In addition, the structure and compaction are not considered in equations (5) and (6). Therefore, they failed to correctly predict the permeability of the undisturbed tailings. These models may be essentially meant for sand, for which they provide good estimates [23].

All the undisturbed tailings samples were calculated by equation (4), which is shown in Figure 13. Most calculated permeability is larger than the measured permeability. The high permeability values calculated by the Kozeny approach can be explained by an imprecise estimation of specific surface area, as well as by the possibility that the model is not valid for some types of soil [22]. In addition, the structure and compaction are not considered in equation (4).

4.2. Models for Permeability Prediction of Tailings

Based on Darcy’s law, the virtual discharge velocity () of the sample becomes

The actual discharge velocity () of the sample becomes larger than the virtual discharge velocity (). The actual discharge velocity () depends on the following expression:

An assemblage of unconnected fluid conduits model the pore system geometry resulting from granular packing of discrete particles [24]. The actual discharge velocity () is given by

Thus, the virtual discharge velocity () is given by

The radius of conduit (R) can be replaced by average pore diameter (D₀). Then, the virtual discharge velocity () is given by

The actual hydraulic gradient (Jh) is determined by the following expression:

The correction coefficient α₂ is given by

Thus, the virtual discharge velocity () is given by

The average pore diameter (D₀) is the key to calculate the permeability coefficient. Based on the research of Institute of Water Resources and Hydropower Research (China), the average pore diameter (D₀) is given by [25]

Thus, the permeability coefficient (K) is given by

where is the virtual discharge velocity; is the actual discharge velocity; n is the porosity; K is the permeability coefficient; Jh is the actual hydraulic gradient; J is the hydraulic gradient; R is the radius of conduit; D₀ is the average pore diameter; is the dynamic viscosity of water, ; d₂₀ is the sample soil particle diameter (cm) corresponding to the cumulative content of 20%; α₂ is the correction coefficient, α₂ = 0.25; and is the gravity acceleration.

4.3. Tailings Classification

Tailings contain a wide range of particle sizes. Different permeability occurs in different particle size ranges and content. Therefore, a better analysis of their permeability requires the tailings to be classified. Based on the research by Thevanayagam [26] and Thevanayagam and Martin [27], the contact state of the soil is affected by FC (fine particle content of particle size below 0.075 mm). And there is a threshold [28]. The permeability coefficient decreases rapidly when the FC (FC = silt content) exceeds 40% in Section 3.1. Benson et al. [29] believe that the permeability coefficient fell off rapidly when the fine content exceeds 40%, which is similar to the test results in Section 3.1. The calculation formula for FCth (the threshold of FC) used to calculate the FCth of iron tailings was proposed by Rahman et al. [28]. The FCth of iron tailings is approximately 40% [21]. Therefore, the iron tailings could be classified into two categories according to the FCth.

Figure 6(b) shows that the permeability coefficients increase with the raise in the clay content at first and then they decrease when the clay content exceeds 15%. There is a threshold for clay content, too. It has been figured out by Koltermann and Gorelick [30] and is shown in Figure 14. The threshold of clay content is approximately 15%, and it is similar to the test results in Figure 6(b). The silt content is constant in Figure 14, but the clay content and silt content of iron tailings are increasing together because of the discharge method. The permeability coefficients increase with the increasing clay content when the silt content exceeds 40% or the clay content is less than 15%. The permeability coefficients decrease when the clay content exceeds 15% because the effective void ratio is reduced.

Figure 14: Variation of clay content with porosity.

Iron tailings can be divided into three categories: (1) silt content is less than 40%; (2) silt content is larger than 40% and clay content is less than 15%; and (3) clay content is 15%–30%. Tailings will become clay tailings when the clay content is larger than 30%. Tailings rarely contain more than 30% of clay particles. Therefore, the research has been not conducted in this paper, and the classifications of clay tailings are in need of further study.

4.4. Permeability Coefficient Calculation of the Disturbed Tailings Samples

The permeability of different types of iron tailings should be calculated by multiple methods. 2-1, 2-2, and 2-3 belong to the first type of iron tailings. Their permeability could be calculated by equation (21). The results are shown in Table 1, which becomes more accurate.

Table 1: The measured permeability and calculated permeability of the disturbed tailings.

Number
n
nsilt
nclay
d₂₀ (μm)
Measured permeability (cm/s)
Calculated permeability (cm/s)
Ratio

2-1
0.3955
—
—
74.17
8.80 × 10⁻⁴
7.96 × 10⁻⁴
0.90

2-2
0.4076
—
—
59.73
6.33 × 10⁻⁴
5.65 × 10⁻⁴
0.89

2-3
0.3980
—
—
59.73
6.52 × 10⁻⁴
5.26 × 10⁻⁴
0.81

2-4
0.4146
0.4703
—
15.66
2.43 × 10⁻⁵
1.69 × 10⁻⁵
0.69

2-5
0.2990
—
0.7234
7.91
6.33 × 10⁻⁵
5.54197 × 10⁻⁵
0.88

Ratio = calculated permeability ÷ measured permeability.

The permeability of iron tailings varies when the silt content is larger than 40% and the clay content is less than 15%. Therefore, n should give place to nsilt. d₁₀ is used to calculate the average pore diameter of silt [21]. The permeability of the second iron tailings (2-4) could be calculated by equation (22), and more accurate results were obtained and are shown in Table 1:

where nsilt is the porosity of iron tailings silt particles and esilt is the silt particle void ratio [28, 30, 31].

The permeability of iron tailings changes when the clay content is larger than 15%. Therefore, n should be substituted by nclay. The permeability of the third iron tailings (2-5) could be calculated by equation (23). The results are more accurate and shown in Table 1:

where nclay is the porosity of iron tailings clay particles, eclay is the clay particle void ratio, and CC is the clay content of iron tailings.

4.5. Permeability Coefficient Calculation of the Undisturbed Tailings Samples

The structure of tailings is different from other soils because of the discharge and deposition method. Iron tailings contain coarse and fine layers (Figure 15). The permeability coefficient of the undisturbed tailings samples is more susceptible to fine particles than that of the disturbed tailings samples. Therefore, the permeability coefficients of the undisturbed tailings are less than those of the disturbed tailings, which resulted from a change in the local porosity of the tailings. By calculation, it was found out that the permeability coefficient of the first type of undisturbed iron tailings was mainly affected by n/nsilt. This can be calculated by equation (24). In addition, the permeability coefficients of the second and the third type of undisturbed iron tailings are mainly affected by nsilt/nclay. They can be calculated by equations (25) and (26).

Figure 15: The undisturbed iron tailings samples.

1-1, 1-2, 1-3, 1-4, and 1-6 belong to the first type of iron tailings whose permeability can be calculated by equation (24). The results are shown in Table 2:

Table 2: The measured permeability and calculated permeability of undisturbed tailings.

Number
n
nsilt
nclay
d₂₀ (μm)
Measured permeability (cm/s)
Calculated permeability (cm/s)
Ratio

1-1
0.3641
0.6820
—
58.73
3.21 × 10⁻⁴
2.08 × 10⁻⁴
0.65

1-2
0.3955
0.7598
—
74.17
3.47 × 10⁻⁴
4.14 × 10⁻⁴
1.19

1-3
0.4076
0.7107
—
59.73
3.21 × 10⁻⁴
3.24 × 10⁻⁴
1.01

1-4
0.4056
0.7614
—
72.17
3.17 × 10⁻⁴
4.33 × 10⁻⁴
1.37

1-5
0.4051
0.6438
0.9569
47.36
2.58 × 10⁻⁴
2.88 × 10⁻⁴
1.12

1-6
0.3980
0.6984
—
59.73
3.28 × 10⁻⁴
3.00 × 10⁻⁴
0.92

1-7
0.4146
0.4703
0.9158
15.66
1.21 × 10⁻⁵
8.66 × 10⁻⁶
0.71

1-8
0.2990
0.4499
0.7234
7.91
3.26 × 10⁻⁵
3.45 × 10⁻⁵
1.06

1-9
0.3237
0.4822
0.7656
10.15
5.58 × 10⁻⁵
6.81 × 10⁻⁵
1.22

1-10
0.3606
0.5010
0.7862
9.2
2.29 × 10⁻⁵
6.13 × 10⁻⁵
2.68

1-11
0.3914
0.6153
0.8728
22.9
2.40 × 10⁻⁵
1.19 × 10⁻⁵
0.49

1-12
0.3566
0.4972
0.7520
5.71
2.27 × 10⁻⁵
2.14 × 10⁻⁵
0.94

Ratio = calculated permeability ÷ measured permeability.

1-5, 1-7, and 1-11 belong to the second type of iron tailings whose permeability can be calculated by equation (25). The results are shown in Table 2:

1-8, 1-9, 1-10, and 1-12 belong to the third type of iron tailings whose permeability can be calculated by equation (26). The results are shown in Table 2:

Based on the permeability equations of disturbed iron tailings, the permeability equations of undisturbed iron tailings are corrected. The results are more accurate, but the theoretical basis needs further verification.

4.6. Consideration of Compaction Characteristics in Prediction of Permeability of Undisturbed Tailings Samples

The ratio of the first iron tailings is approximately 1 when the pressure is less than 200 kPa. It will increase when the pressure is larger than 200 kPa (Figure 16), which indicates that the calculated permeability is too large. As the pressure increases, the porosity decreases. In addition, the blockage also occurs when the pressure is larger than 200 kPa. The greater the pressure is, the more frequently the blockage occurs [22]. P is pressure (kPa).

Figure 16: Variation of pressure with ratio (ratio = calculated permeability by equation (24) ÷ measured permeability).

The ratio and lgP are fitted when the pressure is larger than 200 kPa. The results are shown in Figure 17. The relationship between ratio change caused by clogging and lgP is linear. Based on this, equation (24) can be corrected to equation (27). The crossplots of the calculated permeability using equation (27) and the measured permeability are shown in Figure 18. It is more accurate than other equations (Terzaghi equation, Hazen equation, and Kozeny equation):

The ratio of the second iron tailings does not change much when the pressure is less than 200 kPa and it will increase when the pressure is larger than 200 kPa (Figure 19), which means that the calculated permeability is too large. As the pressure increases, the porosity decreases. In addition, the blockage also occurs when the pressure is larger than 200 kPa. The greater the pressure is, the more frequently the blockage occurs [22, 32–34]. P is pressure (kPa).

Figure 17: Variation of lgP with ratio (ratio = calculated permeability by equation (24) ÷ measured permeability).

Figure 18: Crossplots of the calculated permeability by equation (27) and the measured permeability.

Figure 19: Variation of pressure with ratio (ratio = calculated permeability by equation (25) ÷ measured permeability).

The ratio and lgP are fitted when the pressure is larger than 200 kPa. The results are shown in Figure 20. The relationship between ratio change caused by clogging and lgP is linear. Based on this, equation (25) can be corrected to equation (28). The crossplots of the calculated permeability using equation (28) and the measured permeability are shown in Figure 21. It is more accurate than other equations (Terzaghi equation, Hazen equation, and Kozeny equation):

The ratio of the third iron tailings is approximately 1 when the pressure is less than 200 kPa. It will increase when the pressure is larger than 200 kPa (Figure 22), which means that the calculated permeability is too large. When the pressure increases, the porosity decreases. In addition, the blockage also occurs when the pressure is larger than 200 kPa. The greater the pressure is, the more frequently the blockage occurs [4, 22, 35–37]. P is pressure (kPa).

Figure 20: Variation of lgP with ratio (ratio = calculated permeability by equation (25) ÷ measured permeability).

Figure 21: Crossplots of the calculated permeability by equation (28) and the measured permeability.

Figure 22: Variation of pressure with ratio (ratio = calculated permeability by equation (26) ÷ measured permeability).

The ratio and lgP are fitted when the pressure is larger than 200 kPa. The results are shown in Figure 23. The relationship between ratio change caused by clogging and lgP is linear. Based on this, equation (26) can be corrected to equation (29). The crossplots of the calculated permeability using equation (29) and the measured permeability are shown in Figure 24. It is more accurate than other equations (Terzaghi equation, Hazen equation, and Kozeny equation):

Figure 23: Variation of lgP with ratio (ratio = calculated permeability by equation (26) ÷ measured permeability).

Figure 24: Crossplots of the calculated permeability by equation (29) and the measured permeability.

The water-flow paths are blocked (Figure 25) after compaction. The critical pressure of iron tailings blockage is 200 kPa. Although the porosity is large, some of the pores are isolated from each other when the pressure is larger than 200 kPa. Porosity is too large for permeability calculation. Therefore, the calculated permeability by porosity is too large (equations (24)–(26)). It is necessary to rectify the permeability calculation equations, and the calculated permeability drawing from the revised equations becomes more accurate (equations (27)–(29)). In fact, the granulometric characteristics necessarily play a vital role in the evolution of the pore interconnections by blocking the water-flow paths and by modifying the morphological parameters [7, 22, 38, 39]. More factors about compression tailings need to be considered. Simultaneously, a more accurate model needs to be built to improve R² in Figures 17, 20, and 23. This requires further research in the future.

Figure 25: Evolution of water-flow paths with compaction.

5. Conclusion

The stability of iron tailings dam is affected by the permeability of iron tailings that varies from other soils. Accurate calculations of the iron tailings permeability cannot be obtained by the prediction equations (Terzaghi equation, Hazen equation, and Kozeny equation):

(1)Tailings at different locations on the tailings dam contain diversified particle sizes because of tailings discharge. The classification of iron tailings is desired to accurately calculate the permeability. Then, the iron tailings falls into three categories: (1) silt content is less than 40%; (2) silt content is larger than 40% and clay content is less than 15%; and (3) clay content is 15%–30%. Iron tailings will become clay tailings when the clay content is larger than 30%, which rarely happens. Therefore, the research has been not conducted in this paper and the classification of clay tailings requires further research in the future.(2)Three equations have been proposed to calculate the disturbed iron tailings permeability, and the permeability is accurate. The discharge and deposition method lead to the difference of structure of iron tailings from other soils. Iron tailings contain coarse and fine layers (Figure 15). Therefore, the permeability coefficients of the disturbed tailings are larger than those of the undisturbed tailings. Besides, the permeability coefficient of the first type of undisturbed iron tailings is mainly affected by n/nsilt, while the second and the third type of it are mainly affected by nsilt/nclay. Three equations have been proposed to calculate the three types of undisturbed iron tailings permeability, and the permeability is accurate.(3)The water-flow paths get blocked (Figure 25) after compaction. The critical pressure of iron tailings blockage is 200 kPa. Although the porosity is large, some of the pores are isolated from each other when the pressure becomes larger than 200 kPa. Thus, the conclusion can be drawn that the porosity is more than appropriate for the permeability calculation and the calculated permeability is too large (equations (24)–(26)). It is of importance to correct the permeability calculation equations, and the permeability by the revised equations is getting more accurate (equations (27)–(29)). In fact, the granulometric characteristics necessarily play an essential role in the evolution of the pore interconnections by blocking the water-flow paths and modifying the morphological parameters. This requires further research in the future.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare no conflicts of interest.

Acknowledgments

This research was mainly supported by the National Natural Science Foundation of China (51774137) and National Key Technologies Research & Development Program (2017YFC0804609).

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