# Experimental Analysis on Permeability Characteristics of Iron Tailings

Authors: Deqing Gan; Xi Yang; Yunpeng Zhang
Journal: Mathematical Problems in Engineering
 (2019)

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## Abstract

The permeability characteristics of iron tailings are one of the important factors affecting the stability of the tailings dam. The permeability properties of undisturbed iron tailings and disturbed iron tailings were analyzed from various aspects such asFC value, gradation, particle size, specific surface area, and interparticle void ratio with water head test in laboratory. The results show that the permeability coefficients of undisturbed iron tailings and disturbed iron tailings are affected by the fine particles content (FC). The threshold of fine content is about 40%. The traditional formulas for calculating the permeability coefficient are applied. But the results are inaccurate. The relationship between permeability coefficient of the iron tailings (undisturbed iron tailings and disturbed iron tailings) and the nonuniform coefficient (Cu), the curvature coefficient (Cc), the average particle size, the weighted average particle size, the specific surface area, and the skeleton void ratio (es) is nonlinear. It is difficult to characterize the change of permeability coefficient when the fine content is large. However, the relationship between permeability coefficient of the iron tailings (undisturbed iron tailings and disturbed iron tailings) and the effective particle size and silt particles void ratio (ef) is linear. A formula was developed for the determination of permeability coefficient of iron tailings by analyzing the effective particle size and silt particles void ratio. And it is more accurate. The permeability coefficients of disturbed samples are slightly larger than the permeability coefficients of undisturbed sample. This is due to the destruction of the sedimentary structure of the tailings and increasinge. Maybe theRin the new formula is affected by the structure of iron tailings. This requires further research.


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## Body

## 1. Introduction

Permeability is one of the important factors affecting the stability of tailings dam. The upstream type is the main form of Chinese tailings dams. Due to the difference in tailings particle size and discharge mode, the fine content at different positions of the tailings dam is different, which will inevitably lead to the change of the permeability characteristics of the tailings. The stability of the tailings dam will be affected by the change of the permeability characteristics. Therefore, it is important to carry out the study on the permeability characteristics of tailings with different fine content.At present, the influence of fine sand content on its properties has been studied by some scholars [1–4]. The void ratio caused by the change of fine sand content is an important reason for the change of its properties. The strength parameters and soil-water characteristics of sand under the change of clay content are analyzed by Naser. It is believed that when the clay content exceeds 40%, the above two properties are not changed [5]. The dynamic characteristics of sand under the change of clay content are analyzed by Liu Xuezhu, Zhu Jianqun, Heng Chaoyang, and Zhang Chao [6–9]. The relationship between the dynamic strength and the clay content is obtained. The liquefaction process of silt under the change of fine content is studied by Zeng Changnv [10]. The consolidated undrained triaxial test under the change of silt content is operated by V.T.A.Phan. It is determined that the critical content of the silt is 50%. By studying the tailings materials under different fine contents, Zhang Chao and Yang Chun found that the copper tailings have the best liquefaction resistance when the fine granule content is 35% [11]. At present, the research on the properties of sand under the change of fine content mainly focuses on the strength parameters and liquefaction resistance. The research on the permeability characteristics under the change of fine content is less. In particular, the study on the permeability characteristics of tailings under different fine particle contents is rarely reported.The compressibility and permeability of Bangkok clay have been studied by Suksun Horpibulsuk [12]. The measured permeability values are compared to the values empirically deduced from the cone penetration test. Then the permeability coefficients of tested sand are empirically obtained by Amr F. Elhakim [13]. H. Bayesteh presents an analysis of the association between the coefficient of permeability of active clay and its porosity and tortuosity [14]. The stress dependent permeability of unsaturated clay has been measured by Harsha Vardhan. A 2-D model has been proposed for experts to monitor the permeability property of unsaturated clay [15]. But the permeability of iron tailings has not been analyzed clearly.The permeability has always been an important topic in geotechnical engineering research. The permeability coefficient is the most important indicator for characterizing the permeability characteristics. The change characteristics are directly related to the safety of the tailings dam. In most of cases, permeability coefficient is usually determined from soil water characteristic curve based on analytical approaches proposed by Genuchten [16] and Fredlund and Xing [17]. The relation of grain size and permeability is investigated by Shepherd, R.G. A method of regression estimation of permeability is provided by him [18]. The relation of d10 and permeability is investigated by Hazen. Then Hazen formula is found by him [19]. Patrick J. Kamann expands an existing fractional-packing model for porosity to represent mixtures in which finer grains approach the size of the pores that would exist among the coarser grains alone [20]. Alternatively, permeability coefficient can be also estimated from soil properties, which are commonly known as pedotransfer functions [21] and are mainly utilized in agricultural and environmental science [22]. Besides these, soft computing methods (artificial neural network (ANN) and support vector regression (SVR)) were also used to develop models for predicting the permeability for various types of soil [23–26]. A lot of permeability coefficient calculation formulas are proposed by some scholars. The more famous ones are the Terzaghi formula, Hazen formula, and Kozeny formula [27–32]. There is only particle size which has been considered by Hazen formula. The influence of void ratio and particle size on the permeability coefficient has been considered by Terzaghi formula and Kozeny formula. But the change of effective void ratio under the influence of structure and fine content has not been considered. The tailing contains more fine particles and forms a layered structure during the deposition process. Therefore, the applicability of the above formulas is not clear.The Terzaghi formula is as follows:(1)K=2d102e2The Hazen formula is as follows:(2)K=2d102The Kozeny formula is as follows:(3)K=780n31-n2d92where K is the permeability coefficient of the sample soil at 20°C; n is the porosity of the sample soil; e is the void ratio of the sample soil; d9 and d10 are, respectively, the sample soil particle diameter (mm) corresponding to the cumulative content of 9% and 10%.As a kind of special soil, the permeability of iron tailings is not clear. If the existing formula is used to calculate the permeability coefficient, the results may be not accurate. Therefore, it is necessary to verify the accuracy of the existing formula and establish a calculation model for the permeability coefficient of iron tailings. In this paper, the permeability properties of iron tailings were analyzed byFC (fine particle content of particle size below 0.075mm), gradation, particle size, specific surface area, and void ratio. A new formula for calculating the permeability coefficient of iron tailings is proposed. It is more accurate to calculate the permeability coefficient of iron tailings. In addition, it is important for the stability analysis of tailings dams.


## 2. Materials and Experimental Setup

### 2.1. Preparation of Experimental Samples

The tailings samples used in the test were taken from the Chenkeng tailings reservoir in Fujian Province, China. Apply Vaseline to the inner wall of the ring cutter. Then insert the ring cutter into the sampler before sampling. The diameter of ring cutter is 61.8mm. The height of ring cutter is 40mm. 4 ring cutters can be placed in the sampler. The samplers are used to take the iron tailings sample at different distances from the tailings dam. The samplers and sampling points are shown in Figure1. The sampler must be sealed quickly after sampling. 8 groups of undisturbed iron tailings samples are obtained. The gradation curves are shown in Figure 2. The dry density of the samples is about 2.10 g/cm3.Figure 1
The sampler and sampling points.Figure 2
Gradation curves of iron tailings with different fines content.


### 2.2. Experimental Setup

Experiments were conducted using a TST-55 permeameter that consists of a cutting ring, two porous stones, a lantern ring, a top cover, a bottom cover, and several screws, as shown in Figure3. A cutting ring is inside the TST-55 permeameter and is used to hold the sample. Two porous stones are placed above and below the cutting ring to block sand loss. A lantern ring is used to block water. A top cover, a bottom cover, and several screws are used to fix the sample.Figure 3
TST-55 permeameter.Remove the sealing material before testing. The saturated sample is put into the TST-55 permeameter. The air inside the permeator must be drained. Figure4 shows a schematic of the experimental setup. A steel tape was affixed vertically to a wall. Then, a glass tube with 10 mm diameter and 1.4 m length was vertically affixed to the steel tape. A hose was used to connect the lower end of the tube to the inlet of the permeameter. The permeameter was horizontally installed on a small platform that was 0.1 m above the ground. 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. Before starting a test, the bubbles in the permeameter and tube had to be completely removed by injecting tap water and shaking the tube.Figure 4
Schematic plot of experimental setup.Based on Darcy's law, the permeability coefficient can be given as(4)K=2.3ηTaLη20At2-t1log⁡H1H2where a is the cross-sectional area of the tube (cm2); L is the height of sample (cm); t1 and t2 are the start and end time where water inside the tube falls from H1 to H2 (s); H1 is the initial water head, and H2 is the final water head (cm); ηT is the dynamic viscosity of water atT°C, and η20 is the dynamic viscosity of water at 20°C (kPas).After setting the initial head, the time corresponding to the different water head heights and the water temperature should be recorded. This is repeated 4 times. Finally, according to formula (4), the permeability coefficient of the undisturbed iron tailings is calculated. The average value is taken [33].After completing the test of the undisturbed iron tailings, all undisturbed iron tailings samples are dried and made into a disturbing sample having the same dry density as the undisturbed iron tailings samples. Then the test of the disturbed iron tailings is performed. The method is the same as the undisturbed iron tailings.


## 2.1. Preparation of Experimental Samples

The tailings samples used in the test were taken from the Chenkeng tailings reservoir in Fujian Province, China. Apply Vaseline to the inner wall of the ring cutter. Then insert the ring cutter into the sampler before sampling. The diameter of ring cutter is 61.8mm. The height of ring cutter is 40mm. 4 ring cutters can be placed in the sampler. The samplers are used to take the iron tailings sample at different distances from the tailings dam. The samplers and sampling points are shown in Figure1. The sampler must be sealed quickly after sampling. 8 groups of undisturbed iron tailings samples are obtained. The gradation curves are shown in Figure 2. The dry density of the samples is about 2.10 g/cm3.Figure 1
The sampler and sampling points.Figure 2
Gradation curves of iron tailings with different fines content.


## 2.2. Experimental Setup

Experiments were conducted using a TST-55 permeameter that consists of a cutting ring, two porous stones, a lantern ring, a top cover, a bottom cover, and several screws, as shown in Figure3. A cutting ring is inside the TST-55 permeameter and is used to hold the sample. Two porous stones are placed above and below the cutting ring to block sand loss. A lantern ring is used to block water. A top cover, a bottom cover, and several screws are used to fix the sample.Figure 3
TST-55 permeameter.Remove the sealing material before testing. The saturated sample is put into the TST-55 permeameter. The air inside the permeator must be drained. Figure4 shows a schematic of the experimental setup. A steel tape was affixed vertically to a wall. Then, a glass tube with 10 mm diameter and 1.4 m length was vertically affixed to the steel tape. A hose was used to connect the lower end of the tube to the inlet of the permeameter. The permeameter was horizontally installed on a small platform that was 0.1 m above the ground. 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. Before starting a test, the bubbles in the permeameter and tube had to be completely removed by injecting tap water and shaking the tube.Figure 4
Schematic plot of experimental setup.Based on Darcy's law, the permeability coefficient can be given as(4)K=2.3ηTaLη20At2-t1log⁡H1H2where a is the cross-sectional area of the tube (cm2); L is the height of sample (cm); t1 and t2 are the start and end time where water inside the tube falls from H1 to H2 (s); H1 is the initial water head, and H2 is the final water head (cm); ηT is the dynamic viscosity of water atT°C, and η20 is the dynamic viscosity of water at 20°C (kPas).After setting the initial head, the time corresponding to the different water head heights and the water temperature should be recorded. This is repeated 4 times. Finally, according to formula (4), the permeability coefficient of the undisturbed iron tailings is calculated. The average value is taken [33].After completing the test of the undisturbed iron tailings, all undisturbed iron tailings samples are dried and made into a disturbing sample having the same dry density as the undisturbed iron tailings samples. Then the test of the disturbed iron tailings is performed. The method is the same as the undisturbed iron tailings.


## 3. Test Results

### 3.1. The Influence of Fine Particle Content on Permeability Coefficient

The permeability coefficients of undisturbed iron tailings and disturbed iron tailings under different fine particles contents are shown in Figure5. It can be seen from Figure 5 that as theFC value increases, the permeability coefficient decreases. The curve can be divided into two stages. When theFC is less than about 40%, the permeability coefficient decreases sharply. When theFC value exceeds 40%, the permeability coefficient is basically not changed greatly. It decreases slowly. Nagaraj believes that when theFC value exceeds 40%, the permeability coefficient does not change greatly. This is basically consistent with this test phenomenon [34].Figure 5
Curve between permeability coefficient andFC.


### 3.2. The Influence of Particle Gradation on Permeability Coefficient

Particles gradation is one of the important factors affecting soil permeability coefficient. The uniformity coefficient (Cu) and the curvature coefficient (Cc) are important indicators for evaluating the uniformity and continuity of the particles. The effect of the uniformity coefficient (Cu) on the permeability coefficient is shown in Figure 6. The curve is also divided into two stages. WhenCu is small, the permeability coefficient decreases rapidly with the increase of theCu. WhenCu exceeds 5, the permeability coefficient remains basically the same. TheCu is calculated by the following formula(5)Cu=d60d10where d60 is the sample soil particle diameter (mm) corresponding to the cumulative content of 60%, as d10 was already defined above.Figure 6
Curve between permeability coefficient andCu.The effect of the curvature coefficientCc on the permeability coefficient is shown in Figure 7. The trend is similar to Figure 6. TheCc is calculated by the following formula(6)Cc=d302d60×d10where d30 is the sample soil particle diameter (mm) corresponding to the cumulative content of 30% and the other parameters were previously defined.Figure 7
Curve between permeability coefficient andCc.


### 3.3. The Influence of Particle Size and Specific Surface Area on Permeability Coefficient

d 50 is an important characteristic particle size; there is a great influence on the role of the skeleton particles in the infiltration process. The trend of the permeability coefficient with the average particle size (d50) is shown in Figure 8. As the average particle size increases, the amount of skeleton particles in the undisturbed iron tailings increases, the pores become larger, and the permeability becomes stronger. When the average particle size is less than 0.095 mm, the permeability coefficient does not change much. When the average particle diameter is larger than 0.095 mm, the permeability coefficient sharply increases.Figure 8
Curve between permeability coefficient andd50.The effect of the weighted average particle size on the permeability coefficient is similar to the average particle size. As shown in Figure9, when the weighted average particle diameter is less than 0.11 mm, the permeability coefficient is slowly increased. When the weighted average particle diameter is larger than 0.11 mm, the permeability coefficient is sharply increased.Figure 9
Curve between permeability coefficient and average weighted particle size.There is a good linear relationship between the effective particle size (d10) and permeability coefficient. As shown in Figure 10, the permeability coefficient increases with the increase of the effective particle size.Figure 10
Curve between permeability coefficient andd10.As shown in Figure11, the permeability coefficient decreases with increasing specific surface area. However, the overall change is relatively smooth. There is no particularly obvious inflection point.Figure 11
Curve between permeability coefficient and specific surface area.


### 3.4. The Influence of Skeleton Void Ratio on Permeability Coefficient

The relationship between the permeability coefficient and the void ratio is shown in Figure12. There are three stages. The first stage: as the void ratio increases, the permeability coefficient increases. The second stage: although the void ratio is similar, the permeability coefficient is quite different. The third stage: as the void ratio increases, the permeability coefficient remains remarkably constant.Figure 12
Curve between permeability coefficient ande.Thees is calculated by the following formula(7)es=e+FCe-FCwhere es is the skeleton void ratio; e is the void ratio; FC is the fine particle content of particle size below 0.075mm.The curve of the permeability coefficient with the skeleton void ratio (es) is shown in Figure 13. It is mainly divided into two processes. When es is less than 2, the permeability coefficient decreases rapidly as it increases. When it is greater than 2, the permeability coefficient decreases slowly as it increases.Figure 13
Curve between permeability coefficient andes.Theef is calculated by the following formula (8)ef=eFCwhere ef is the silt particles void ratio; e is the void ratio;FC is the fine particle content of particle size below 0.075mm.The curve of the permeability coefficient with the silt particles void ratio (ef) is shown in Figure 14. There is a good linear relationship between ef and permeability coefficient. The permeability coefficient increases as ef increases.Figure 14
Curve between permeability coefficient andef.


## 3.1. The Influence of Fine Particle Content on Permeability Coefficient

The permeability coefficients of undisturbed iron tailings and disturbed iron tailings under different fine particles contents are shown in Figure5. It can be seen from Figure 5 that as theFC value increases, the permeability coefficient decreases. The curve can be divided into two stages. When theFC is less than about 40%, the permeability coefficient decreases sharply. When theFC value exceeds 40%, the permeability coefficient is basically not changed greatly. It decreases slowly. Nagaraj believes that when theFC value exceeds 40%, the permeability coefficient does not change greatly. This is basically consistent with this test phenomenon [34].Figure 5
Curve between permeability coefficient andFC.


## 3.2. The Influence of Particle Gradation on Permeability Coefficient

Particles gradation is one of the important factors affecting soil permeability coefficient. The uniformity coefficient (Cu) and the curvature coefficient (Cc) are important indicators for evaluating the uniformity and continuity of the particles. The effect of the uniformity coefficient (Cu) on the permeability coefficient is shown in Figure 6. The curve is also divided into two stages. WhenCu is small, the permeability coefficient decreases rapidly with the increase of theCu. WhenCu exceeds 5, the permeability coefficient remains basically the same. TheCu is calculated by the following formula(5)Cu=d60d10where d60 is the sample soil particle diameter (mm) corresponding to the cumulative content of 60%, as d10 was already defined above.Figure 6
Curve between permeability coefficient andCu.The effect of the curvature coefficientCc on the permeability coefficient is shown in Figure 7. The trend is similar to Figure 6. TheCc is calculated by the following formula(6)Cc=d302d60×d10where d30 is the sample soil particle diameter (mm) corresponding to the cumulative content of 30% and the other parameters were previously defined.Figure 7
Curve between permeability coefficient andCc.


## 3.3. The Influence of Particle Size and Specific Surface Area on Permeability Coefficient

d 50 is an important characteristic particle size; there is a great influence on the role of the skeleton particles in the infiltration process. The trend of the permeability coefficient with the average particle size (d50) is shown in Figure 8. As the average particle size increases, the amount of skeleton particles in the undisturbed iron tailings increases, the pores become larger, and the permeability becomes stronger. When the average particle size is less than 0.095 mm, the permeability coefficient does not change much. When the average particle diameter is larger than 0.095 mm, the permeability coefficient sharply increases.Figure 8
Curve between permeability coefficient andd50.The effect of the weighted average particle size on the permeability coefficient is similar to the average particle size. As shown in Figure9, when the weighted average particle diameter is less than 0.11 mm, the permeability coefficient is slowly increased. When the weighted average particle diameter is larger than 0.11 mm, the permeability coefficient is sharply increased.Figure 9
Curve between permeability coefficient and average weighted particle size.There is a good linear relationship between the effective particle size (d10) and permeability coefficient. As shown in Figure 10, the permeability coefficient increases with the increase of the effective particle size.Figure 10
Curve between permeability coefficient andd10.As shown in Figure11, the permeability coefficient decreases with increasing specific surface area. However, the overall change is relatively smooth. There is no particularly obvious inflection point.Figure 11
Curve between permeability coefficient and specific surface area.


## 3.4. The Influence of Skeleton Void Ratio on Permeability Coefficient

The relationship between the permeability coefficient and the void ratio is shown in Figure12. There are three stages. The first stage: as the void ratio increases, the permeability coefficient increases. The second stage: although the void ratio is similar, the permeability coefficient is quite different. The third stage: as the void ratio increases, the permeability coefficient remains remarkably constant.Figure 12
Curve between permeability coefficient ande.Thees is calculated by the following formula(7)es=e+FCe-FCwhere es is the skeleton void ratio; e is the void ratio; FC is the fine particle content of particle size below 0.075mm.The curve of the permeability coefficient with the skeleton void ratio (es) is shown in Figure 13. It is mainly divided into two processes. When es is less than 2, the permeability coefficient decreases rapidly as it increases. When it is greater than 2, the permeability coefficient decreases slowly as it increases.Figure 13
Curve between permeability coefficient andes.Theef is calculated by the following formula (8)ef=eFCwhere ef is the silt particles void ratio; e is the void ratio;FC is the fine particle content of particle size below 0.075mm.The curve of the permeability coefficient with the silt particles void ratio (ef) is shown in Figure 14. There is a good linear relationship between ef and permeability coefficient. The permeability coefficient increases as ef increases.Figure 14
Curve between permeability coefficient andef.


## 4. Discussion

The phenomenon of Figures5, 6, 7, 8, 9, and 11 is mainly affected by the fine particles content. In the case of the same dry density, the permeability decreases with the increase of fine particles content. Moreover, there is a fine particle content threshold during the descent process. When the fine particles content exceeds this threshold, there will be a different trend of the permeability coefficient. Thevanayagam [35] and Martin [36] found that if theFC (fine particles content of particle size below 0.075 mm) is different, the contact state of the soil is also different. When the change ofFC value causes the change of sand properties, there must be a threshold. Rahman [37] proposed the calculation formula for FCth:(9)FCth=0.40×11+exp⁡α-βχ+1χwhere α and β are shape correction parameters; they can be taken as 0.50 and 0.13, respectively, χ=D10/d50, D10 is the effective particle size of pure sand soil, and d50 is the average particle size of pure fine-grained soil.TheFCth of the iron tailings is calculated by formula (9). The results are shown in Table 1. The FCth of iron tailings is about 40%. This is substantially consistent with the phenomena appearing in Figures 5, 6, 7, 8, 9, and 11.Table 1
Calculation results ofFCth.
Number F C t h Number F C t h 1 37.84% 5 40.66% 2 39.18% 6 39.44% 3 37.83% 7 39.60% 4 38.33% 8 42.87%What is the principle of the phenomenon in Figure12? This is mainly due to the influence of fine particles content on the void ratio.In the first stage (FC28.55%,FC25.17%,FC21.45%), the fine particles content of iron tailings is less, and the fine particles are filled in the pores between the coarse particles. When the fine particles content is decreased, the void ratio is increased and the permeability coefficient is increased.In the second stage (FC21.45%,FC37.89%,FC41.37%), the fine particles content of iron tailings begins to increase. But their void ratios are similar. Their permeability coefficients are quite different. As shown in Figure 15, the void ratio decreases first and then increases with the increasing of the fine particles content (FC). The void ratio of iron tailings with about 20% fine particles content is the same as those with about 40% fine particle content in Figure 12. It is basically consistent with the data in Figure 15. Although the void ratios are similar, the pore sizes are different. When the fine particles content is small, the fine particles are loosely filled between the coarse particles. At this time, there are many large pores. When the fine particles content is large, the coarse particles will be wrapped with fine particles. At this time, more small pores are formed. Although the total void ratios are similar, the permeability coefficients are different. The permeability coefficients are affected by the pore size.Figure 15
Relationships between void ratio and volume fraction of fine particle (8, 4, 3, and 2 are the ratio of the particle size of the coarse and fine particles).As shown in Figure16, the outer side of the soil particles is covered with a layer of bound water film, which results in less effective pores. Fine particles are more likely to form small pores. If there are more fine particles, there will be more small pores. When the total void ratios are the same, the total effective void ratio of the small pore sample is smaller than the total effective void ratio of the large pore sample because the small pores are more easily affected by the water film. Further, the permeability coefficient of the iron tailings with larger fine particle content is smaller. The permeability coefficient of the iron tailings with less fine particle content is larger [38–40].Figure 16
Distribution of particle of loose soil.In the third stage (FC41.37%,FC52.3%,FC56.34%,FC79.77%), the fine particles content of the iron tailings is further increased. Although the void ratio is increased, the effective void ratio is reduced. At this time, the iron tailings pores are mainly composed of small pores and extremely small pores. Therefore, the permeability coefficient is slowly decreased as the void ratio increases.The iron tailings sample is shown in Figure17. Iron tailings are formed by multiple discharges and deposits. During the settling process, coarse particles are deposited in the lower portion and fine particles are deposited in the upper portion. Therefore, iron tailings are a multilayered structure of coarse and fine particles. In the process of layer-by-layer infiltration of water from top to bottom, it penetrates faster in the coarse particle layer and slower in the fine particle layer. This leads to a slower penetration of iron tailings. Its penetration rate is mainly controlled by fine particles and their pores. Therefore, there is a high linear correlation between d10, ef, and the permeability coefficient. As shown in Figures 10 and 14, the iron tailings are considered as a whole byCc,Cu, specific surface area, d50, average weighted particle size, and es. The change in its internal structure has not been taken into account. So their linear correlation with the permeability coefficient is bad. A calculation formula for the permeability coefficient using d10 and ef is more suitable for iron tailings.Figure 17
The iron tailings sample.The permeability coefficient is affected by the particle shape and void ratio. The essential features can better be reflected byd10 and ef. The permeability coefficient increases with increasing ef×d10. Based on the forms of other formulas, the calculation formula for the permeability coefficient of iron tailings is established as the following formula(10)K=Refd10where R is a dimensionless coefficient.The fitting relationship between the product (d10 and ef) and the permeability coefficient is shown in Figure 18. The fitting correlation coefficient is higher than that of d10 and ef alone.Figure 18
Curve between permeability coefficient andef×d10.The dimensionless coefficient R in the formula can be derived by substituting the test data into the established calculation formula (10) for inversion calculation. When R is 5.5×10−3, the calculated permeability coefficients of undisturbed iron tailings are the closest to the actual measured values. The permeability coefficient is calculated by formula (10). The calculation results are compared with the calculation results of the traditional formula (such as Terzaghi formula, Hazen formula, and Kozeny formula). The comparison results are shown in Table 2.Table 2
Comparison between measured values and predictive results of permeability coefficient using different formulas for undisturbed iron tailings.
Measured value (cm/s) d 10 (mm) e f Calculated value by formula (10) (cm/s) Calculated value by Terzaghi formula (cm/s) Calculated value by Hazen formula (cm/s) Calculated value by Kozeny formula (cm/s) 7.00×10−4 0.04278 3.02 7.11×10−4 1.54×10−3 3.66×10−3 2.08×10−1 5.16×10−4 0.04127 2.50 5.68×10−4 1.35×10−3 3.41×10−3 1.73×10−1 2.58×10−4 0.02617 1.71 2.46×10−4 5.72×10−4 1.37×10−3 7.14×10−2 4.92×10−4 0.03019 2.10 3.49×10−4 6.56×10−4 1.82×10−3 6.42×10−2 2.40×10−5 0.00556 1.54 4.70×10−5 2.50×10−5 6.18×10−5 2.89×10−3 2.29×10−5 0.00238 1.31 1.71×10−5 5.29×10−6 1.13×10−5 6.83×10−4  2.28×10−5 0.00254 1.25 1.74×10−5 6.39×10−6 1.29×10−5 8.37×10−4 1.21×10−5 0.00832 0.96 4.40×10−5 8.14×10−5 1.38×10−4 1.10×10−2For Kozeny’s formula the result was expected, as this formula is valid for coarse grained soils. The calculation result of the Kozeny formula differs greatly from the measured value. The results differ by 2 to 3 orders of magnitude from the measured value. It is not applicable to the calculation of permeability coefficient of iron tailings. The Hazen formula is more accurate in calculating the fine iron tailings. However, for iron tailings samples with low fines content, the calculation results differ by 1 order of magnitude from the measured value. If the Terzaghi formula is applied to calculate the permeability coefficient of iron tailings with moderate fine particle content, the results are more accurate. However, when the content of fine particles is small or large, the calculation results differ by 1 order of magnitude from the measured value. If the permeability coefficient of iron tailings is calculated by formula (10) in this paper, the results are more accurate. The calculated results keep on the same order of magnitude as the measured values.The dimensionless coefficient R in the formula can be derived by substituting the test data into the established calculation formula (10) for inversion calculation. WhenR is 5.95×10−3, the calculated permeability coefficients of disturbed iron tailings are the closest to the actual measured values. The permeability coefficient is calculated by formula (10). The calculation results are compared with the calculation results of the traditional formula (such as Terzaghi formula, Hazen formula, and Kozeny formula). The comparison results are shown in Table 3.Table 3
Comparison between measured values and predictive results of permeability coefficient using different formulas for disturbed iron tailings.
Measured value (cm/s) d 10 (mm) e f Calculated value by formula (10) (cm/s) Calculated value by Terzaghi formula (cm/s) Calculated value by Hazen formula (cm/s) Calculated value by Kozeny formula (cm/s) 8.00×10−4 0.04278 3.02 8.16×10−4 1.73×10−3 3.66×10−3 2.43×10−1 6.76×10−4 0.04127 2.50 6.59×10−4 1.55×10−3 3.41×10−3 2.08×10−1 6.52×10−4 0.02617 1.71 4.16×10−4 7.97×10−4 1.82×10−3 8.28×10−2 3.78×10−4 0.03019 2.10 2.82×10−4 6.45×10−4 1.37×10−3 8.35×10−2 7.60×10−5 0.00556 1.54 5.41×10−5 2.83×10−5 6.18×10−5 3.39×10−3 6.33×10−5 0.00238 1.31 1.93×10−5 5.76×10−6 1.13×10−5 7.63×10−4  6.43×10−5 0.00254 1.25 1.99×10−5 7.14×10−6 1.29×10−5 9.65×10−4 4.31×10−5 0.00832 0.96 5.02×10−5 9.05×10−5 1.38×10−4 1.25×10−2Formula (10) is more accurate for calculating the permeability coefficient, whether it is a disturbed sample or an undisturbed sample. The permeability coefficients of disturbed samples are slightly larger than the permeability coefficients of undisturbed sample. This is due to the destruction of the sedimentary structure of the tailings and increasinge. TheR of disturbed iron tailings is bigger than theR of undisturbed iron tailings. Maybe theR is affected by the structure of iron tailings. This requires further research.


## 5. Conclusion

(1) The permeability coefficient of the undisturbed iron tailings is obviously affected by the fine particles content (FC). When the fine particles content is less than 40%, the permeability coefficient decreases rapidly with the increase of fine particles content. When the fine particle content is more than about 40%, the permeability coefficient tends to decrease slowly and tends to be stable.(2) There is an obvious nonlinear relationship between the permeability coefficient of the undisturbed iron tailings andCu,Cc, average particle size, weighted average particle size, specific surface area, and skeleton void ratio (es). However, d10 and ef respectively show a good correlation with the permeability coefficient of iron tailings. The permeability coefficient of iron tailings can be predicted by d10 and ef.(3) The calculation results of the Kozeny formula differ greatly from the measured value. The results differ by 2 to 3 orders of magnitude from the measured value. It is not applicable to the calculation of permeability coefficient of iron tailings. The Hazen formula is more accurate in calculating the fine iron tailings. However, for iron tailings samples with low fines content, the calculation results differ by 1 order of magnitude from the measured value. If the Terzaghi formula is applied to calculate the permeability coefficient of iron tailings with moderate fine particle content, the results are more accurate. However, when the content of fine particles is small or large, the calculation results differ by 1 order of magnitude from the measured value. If the permeability coefficient of iron tailings is calculated by formula (10) in this paper, the results are more accurate. The calculated results keep on the same order of magnitude as the measured values. It is more accurate to calculate the permeability coefficient of iron tailings. It is significant for the stability analysis of tailings dams.(4) In this paper, the permeability characteristics of undisturbed iron tailings are analyzed. It is of certain significance to the stability analysis of the tailings dam under seepage action. However, the permeability characteristics of the iron tailings at the microscopic scale have not been analyzed. The relevant research work needs to be further carried out.



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*Source: 6539846-2019-03-28.xml*