Hydraulic anisotropy ratio of undisturbed tailings samples

C_c

compression index

C_v

coefficient of consolidation

e

void ratio

e_f

final void ratio

e_i

initial void ratio

e_max

maximum void ratio

e_min

minimum void ratio

e_n

natural void ratio

F_c

fines content

F_ch_s

fines content in the horizontal sample

F_cv_s

fines content in the vertical sample

G_s

specific gravity

h

hydraulic head

i

hydraulic gradient

$k⊥$

permeability coefficient in the direction perpendicular to the stratification plane

k_‖

permeability coefficient parallel to the stratification plane

k_h

permeability in the horizontal direction

k_v

permeability in the vertical direction

r_k

hydraulic anisotropy ratio

U

discharge velocity

β

Skempton’s parameter

ΔF_c

difference in the fines content

σ′

effective stress

ω

natural water content

The hydraulic conductivity or permeability of a porous medium is a measure of the ease with which a fluid flows through the medium; the magnitude of the permeability is associated with the structure of the voids in the medium (Gu et al., 2022). Permeability is one of the properties that present great natural variability in soils, so it is common to find differences of up to several orders of magnitude among the permeabilities of the materials of the same geological formation (López-Acosta, 2017).

In general, soils exhibit variations in their physical and mechanical properties that can be classified in two ways: heterogeneity, which is the variation of a parameter over space within a geological formation; and anisotropy, which is the vector variation of a property at a given point within a geological formation (Clavaud et al., 2008). Soil heterogeneity results from the natural geological processes by which soil is deposited and formed as a geomechanical material (Jamshidi Chenari and Behfar, 2017). In contrast, anisotropy is a natural outcome of the soil’s depositional history and stress history, and can be attributed to both inherent anisotropy and induced anisotropy. Inherent anisotropy refers to the preferential orientation of the soil fabric established during particle deposition and sedimentation, whereas induced anisotropy refers to changes in particle arrangement and orientation caused by the application of external loads (Jamshidi Chenari and Behfar, 2017; Jamshidi Chenari and Mahigir, 2014).

According to Witt and Brauns (1983), there are three main causes of hydraulic anisotropy: macro-stratification, micro-stratification, and the orientation of non-spherical particles. Macro-stratification is caused by changes in materials and depositional conditions over geological time, leading to successive layers with different grain-size distributions, textures, or lithologies. Layers with higher permeability will convey most of the flow under a flow regime parallel to the stratification, whereas layers with lower permeability will govern the flow regime perpendicular to the stratification, thus creating anisotropy (Nordquist, 2015). The microstructure comprises the soil skeleton, interparticle connections, particle contacts, and pore morphology (Xu et al., 2020). Hydraulic anisotropy is therefore largely controlled by the soil’s macro and microstructure. Particle orientation is typically the result of compression, where particles align perpendicular to the principal stress. Several researchers have recognised the significant influence of particle orientation on the magnitude of directional permeability. At the particle scale, hydraulic anisotropy develops due to the tortuosity of the flow path within the soil (Scholes et al., 2007).

The hydraulic anisotropy ratio (r_k) is commonly defined as the ratio of the permeability coefficient parallel to the stratification plane $k∥$ (horizontal flow) and the permeability coefficient in the direction perpendicular to the stratification plane $k⊥$ (vertical flow); therefore (Bolton et al., 2000; Chan and Kenney, 1973; Scholes et al., 2007):

Since the horizontal permeability is typically greater than the vertical one, the hydraulic anisotropy ratio is usually of a magnitude larger than unity; however, vertical permeability values greater than the horizontal permeability (anisotropy smaller than unity) have been found at shallow depths. Micro-cracks induced by stresses are likely to generate preferential values of vertical permeability (Bolton et al., 2000; Chapuis and Gill, 1989).

Tailings are fine solid residues generated from the beneficiation of minerals by grinding processes in a mineral concentration plant (Orozco, 2010). Their origin begins with the extraction of the mineral, followed by the stages of crushing, grinding, concentration (flotation, leaching, or other methods), and ends with the deposition of the waste in a semi-liquid state, which is transported through pipelines to the deposit (Blight, 2010; Candelaria et al., 2022; ICOLD, 2001; Vick, 1990). During discharge, particles settle according to their size and specific gravity: larger and heavier particles settle more rapidly and closer to the discharge point, while smaller and lighter particles are carried to more distal zones. This depositional mechanism gives tailings deposits a stratified, heterogeneous and anisotropic structure, with layers of different permeabilities and compressibilities that directly influence their hydraulic and mechanical behaviour (Kossoff et al., 2014; Villavicencio et al., 2014).

Permeability is one of the most important properties in the design of tailings dams, as it governs both the consolidation of the material and the water flow conditions within and through the deposit (Bussiere, 2004). Tailings generally exhibit very low permeability values and often display significant anisotropic conditions (López-Acosta and Mendoza-Promotor, 2016). Other factors on which hydraulic anisotropy in tailings dams depends are the milling process, the possible interruption of the disposal site operation, and climatic conditions (Perlea and Botea, 1984).

In the literature, many r_k values are found for clays, sands, and rocks, but few results are available for tailings. Due to their layered nature, tailings dams exhibit considerable variation in permeability between the parallel (⁠$kh$⁠) and the perpendicular (⁠$kv$⁠) directions with respect to stratification (Abadjiev, 1976). In the case of quite uniform sandy beaches that are not sufficiently compacted, and for silty areas deposited underwater, the hydraulic anisotropy ratio is in the range from 2 to 10 (Saad, 2008; Vick, 1990). Transition zones between clean coarse sands and silts show higher anisotropy factors, due to the intermediate layer of finer and coarser particles; for tailings dams where discharge procedures are not well controlled, the anisotropy ratio can be as high as 100 or more (Vick, 1990; Witt and Schönhardt, 2004). The hydraulic anisotropy measured by different researchers in tailings is presented in Table 1.

The hydraulic anisotropy ratio within the tailings dam affects the seepage pattern and influences the position of the water table; due to anisotropy, the phreatic level at the flow discharge point shows a significant increase compared with the isotropic case. Nelson et al. (1977) observed that a small rise in the water table can result in zones of saturation at the face of the reservoir and can affect the overall stability of the reservoir, so that as the accuracy required in water flow models increases, the need to take hydraulic anisotropy into account increases.

Due to the particular characteristics of tailings and the limited information available in the literature regarding the hydraulic anisotropy ratio in this type of material, the main objective of this investigation was to determine in the laboratory the magnitude of the hydraulic anisotropy ratio in undisturbed tailings samples with different fines contents. To this end, constant-head permeability tests were performed, and the results obtained were compared with those reported by other researchers. As part of the experimental programme, the compression index (C_c) and coefficients of consolidation (C_v) were also determined, evaluating the influence of parameters such as fines content, permeability, and void ratio.

The soil studied in this work corresponds to undisturbed tailings samples recovered from three tailings dams located in Mexico.

Table 2 shows a summary of the properties of the tailings studied: natural water content w, [ASTM D2216-19 (ASTM, 2019)]; specific gravity G_s, [ASTM D854-23 (ASTM, 2023)]; fines content, F_c [ASTM D1140-17 (ASTM, 2017b)], and the natural void ratio e_n.

The hydraulic anisotropy ratio (r_k) was assessed in undisturbed tailings samples using a constant-head, flexible-wall permeameter. This device consists of pressure and volume change sensors, as well as a signal conditioning and data acquisition system, as shown in Figures 1(a) and 1(b).

Results of the hydraulic anisotropy ratio of soils and rocks using a variety of laboratory techniques have been reported in the literature (Adams et al., 2016; Chan and Kenney, 1973; Lucero, 2022), as well as of field techniques (Chapuis and Gill, 1989).

To evaluate the hydraulic anisotropy ratio in undisturbed tailings samples, the experimental method of trimming specimens in different directions presented by Chapuis and Gill (1989) has been used; this methodology allows the determination of r_k values in different materials such as clays (Lucero, 2022) and rocks, but it is not known that it has been applied to find r_k in tailings. The procedure consists of first determining the vertical permeability, followed by the horizontal permeability. Once permeability has been measured in both directions, the hydraulic anisotropy ratio (r_k) is calculated. It is important to note that the specimens tested for k_v and k_h were taken from the same Shelby tube but not from the same horizon, since the specimen dimensions do not allow this; however, they were tested under identical stress conditions and hydraulic gradients. Figure 2 shows two specimens of different tailings, trimmed in both directions, to illustrate the highly stratified nature of the material.

The experimental programme to obtain the hydraulic anisotropy ratio consisted of 31 tests, of which 14 were tested in the vertical direction and 17 in the horizontal direction.

The experimental procedure consists of six stages. The first stage is the formation and mounting of samples, where the specimen is worked in the desired direction, in the direction of the field extraction for vertical specimens and in the transverse direction of the field extraction for horizontal specimens. The samples are mounted in the constant head permeability equipment, confined by a latex membrane (Figure 1(c)).

Most of the tailing samples tested had saturation levels above 70%, so to facilitate saturation, water was circulated and saturated with back pressure. To indirectly estimate sample saturation, Skempton’s β was measured, such that the sample is considered saturated when this parameter is equal to or greater than 0.95 [ASTM D4767-11 (ASTM, 2020)].

Because the test is non-destructive during the consolidation phase, all samples were tested at six effective stress levels: σ′ = 19.6, 39.2, 78.5, 156.9, 245.2, and 313 kPa. These stresses were assigned to observe the variation in the void ratio, compressibility parameters, and permeability with stress, as well as to compare the samples, ensuring that all were evaluated under the same experimental conditions. One of the limitations of the equipment is that it is not possible to measure the displacements sustained by the specimen when the effective stress is applied, but a record of the output volumes is kept as established by the standard ASTM D5084-24 (ASTM, 2024); therefore, it is assumed that the total volumetric changes affect only the cross-sectional area of the specimen, leaving the height of the specimen constant.

In the testing stage, the vertical and horizontal permeabilities are determined for each of the effective stresses applied. The test is carried out by applying an upward flow through the specimens, measuring the permeability under four hydraulic heads: h = 150, 217, 284, and 350 cm of water column; the flow rate is calculated from the slope of the time against volumetric change line, as shown in Figure 3.

The permeability as a function of the effective stress applied is obtained by plotting the linear relationship between the discharge velocity U and the hydraulic gradient i; the slope of the line becomes the permeability, as shown in Figure 4. For each effective stress, the hydraulic anisotropy ratio r_k is calculated from Equation 1. After each test, the sample is retrieved and dried for 24 h, and it is then analysed by wet sieving [ASTM D1140-17 (ASTM, 2017b)] to determine its fines content.

Compressibility is a measure of the volume change of tailings in response to an increase in stress. Understanding compressibility parameters (such as the compression index, C_c, or the recompression index, C_s) is essential for the design and operation of tailings dams, as it allows predicting the magnitude and rate of settlements and estimating the dissipation of pore pressures. These factors are crucial for ensuring the static stability of dams, optimising drainage systems, planning growth stages, and preventing failures associated with excessive deformations or critical outlet gradients, both during operation and during dam closure (Bussiere, 2004; Hu et al., 2017).

Hu et al. (2017) analysed the geotechnical properties of four tailings mixtures from the Yuhezhai and Bahuerachi mines, which were tested at stresses of 12.5, 25, 50, 100, 200, 400, 800, and 1600 kPa. For the tailings from the Yuhezhai mine, they obtained C_c values of 0.046 and 0.260, while for the samples from the Bahuerachi mine, they obtained C_c values of 0.025 and 0.085. In another study conducted by Fan et al. (2022), the influence of fines content on the compressibility of tailings mixtures with variable fines content, from 0% to 100%, was determined. The samples were tested at stresses of 90, 180, 390, and 610 kPa, for tailings with between 0 and 50% fines, C_c values between 0.051 and 0.085 were obtained, and for tailings with fines greater than 50%, C_c values between 0.091 and 0.15 were obtained. Figure 5 illustrates the effect of fines content on the compression index (C_c) for the samples tested in this study. For relatively dense samples (e ≤ 1), C_c shows a clear increasing trend with fines content: the sample with the lowest fines content (F_c = 13%) exhibited a C_c = 0.056, whereas for samples with F_c = 100%, C_c ranged from 0.065 to 0.102. In contrast, for looser tailings samples with void ratios greater than one, C_c values ranged from 0.194 to 0.440, indicating significantly higher compressibility. This behaviour is consistent with the findings of Hu et al. (2017) and Fan et al. (2022), who also reported that the compression index increases with fines content. This trend reflects the greater compressibility of fine-grained tailings.

Tailings consolidation results from particle deformation and the expulsion of water or air from voids and is governed by permeability and compressibility (Mosquera, 2013; Vermeulen, 2001; Vick, 1990).

According to Terzaghi, the consolidation process can be divided into primary and secondary phases. Primary consolidation controls the rate of dissipation of excess pore pressures under constant loading, while secondary consolidation is additional deformation under constant loading, even after pore pressure has been completely dissipated, and is associated with grain-to-grain sliding and particle rearrangement (Terzaghi et al., 1996). Primary and secondary consolidation occur simultaneously; however, most of the effects of secondary consolidation in tailings are very small and are often considered insignificant (Vick, 1990; Xu, 2019).

According to Saad (2008), sand tailings (coarse fraction) dissipate excess pore pressure quickly since they usually have high permeability and lower compressibility (according to the results presented in the previous section); consequently, the values of the consolidation coefficient C_v are relatively high. On the other hand, in saturated fine tailings, when subjected to an increase in load, the excess pore pressure generated dissipates much more slowly due to their low permeability and high compressibility, which causes the C_v to decrease. This can be seen in the results shown in Figure 6(a) for the vertical (V-S) and horizontal (H-S) samples; for tailings with fines contents less than 50%, C_v values of 2.6 × 10⁻² to 5 × 10⁻⁵ m²/s were obtained; while for tailings with fines contents greater than 50%, C_v values of the range of 4.5 × 10⁻⁴ to 4.4 × 10⁻⁷ m²/s were obtained.

During consolidation, the void ratio decreases, and permeability and volumetric compressibility typically decrease. The opposing interaction of these two functions determines whether C_v remains constant, increases, or decreases with the void ratio (Fan et al., 2022; Wang et al., 2015). Figure 6(b) shows the influence of the void ratio on C_v for the tailings tested.

The works by Bussiere (2004), Mosquera (2013), Vermeulen (2001), Vick (1990), and Qiu and Sego (2001) report values for the coefficients C_c and C_v for different types of tailings, both for undisturbed and reconstituted samples.

Cubrinovski and Ishihara (2002) used data from more than 300 natural sands (clean sands, sands with fines, and sands with small amounts of clay-sized particles) to assess the influence of fines, grain size composition, and particle shape on the void ratio (e_max − e_min). They found that both e_max and e_min for mixtures of sand with fines decrease as the fines content increases from 0% to about 20%, as small particles fill the gaps between the larger particles. Within the range from 20% to 40% of fines, e_max and e_min show a pattern change indicating a transition from the void-filling process to the solid particle replacement process. In mixtures of sands with fines content greater than 40%, e_max and e_min constantly increase until they reach the highest values corresponding to a fines content of 100%.

Figure 7(a) shows undisturbed tailings samples with fines contents ranging from 13% to 100%, with their initial void ratio (corresponding to σ′ = 19.6 kPa) and final void ratio (σ′ = 313.8 kPa); it can be observed that the tailings show a behaviour similar to that described by Cubrinovski and Ishihara (2002). The void ratios (e_i and e_f) tend to decrease as F_c increases in tailings samples with very low fines content (between 0% and 30%); then, there is a transition zone in the tailings samples with F_c between 40% and 50%, in which e_i and e_f present their lowest value and begin to increase, until they reach the highest values for tailings with F_c equal to 100%.

The highest values of e_i and e_f are related to soils with 100% fines, as can be seen in Figure 7(a). According to Vick (1990), lower void ratios generally correspond to greater depths within a tailings dam, and higher void ratios are generally associated with near-surface materials. Figure 7(b) shows the values of e_i and e_f for tailings with fine contents between 80% and 100%; samples 1, 2, and 3 have the highest void ratios corresponding to the shallowest samples.

As previously mentioned, higher permeability favours elevated C_v values and, consequently, faster consolidation, whereas low permeabilities result in reduced C_v and prolonged dissipation times (Qiu and Sego, 2001). This relationship between C_v and k has direct implications for the stability of tailings deposits; tailings with high permeability and low compressibility promote rapid dissipation of pore pressures, allowing a more stable response under loading. In contrast, tailings with low permeability and reduced C_v cause excess pore pressure to persist for long periods, thereby decreasing effective stresses and increasing the likelihood of structural instability and even static liquefaction phenomena (Mosquera, 2013; Qiu and Sego, 2001; Vermeulen, 2001). Therefore, jointly analysing C_v and k is essential to design drainage strategies, define safe loading rates, and evaluate the short- and long-term stability of tailings dams (Vermeulen, 2001). Figure 8 illustrates this relationship for the tested samples; in tailings with high permeabilities (between 1 × 10⁻⁴ and 1 × 10⁻⁶ m/s; Fell, 2005), C_v values range from 9.4 × 10⁻³ to 4.05 × 10⁻³ m²/s, while in low-permeability tailings C_v values decrease to a range of 4.0 × 10⁻⁴ to 5.9 × 10⁻⁷ m²/s.

Tailings permeability is difficult to generalise; on the average, it varies from five or more orders of magnitude, that is from 10⁻⁴ m/s for clean coarse sands to 10⁻⁹ m/s for consolidated sludge (Vick, 1990). There are important aspects that require consideration, such as the influence of the void ratio, grain size distribution, plasticity, fines content, deposition method, and dam thickness (Mittal, 1975; Vick, 1990). From a geotechnical point of view, tailings are considered to have low to very low hydraulic conductivity (Lambe, 1958).

Hydraulic deposition affects the properties of the tailings, so that the parameters change with distance to the discharge point; material near the discharge point has a void ratio ranging from 0.6 to 1.0, as opposed to the furthest points where the void ratio varies from 1.0 to 1.6 or more (Espinoza, 2005; Jantzer et al., 2008). The tailings generally evidence a loose state (Blight, 2010).

Tailings are more compressible compared with natural soils of equivalent grain size distribution, due to the loose state of deposition and their high angularity; therefore, tailings require measurements of permeability at various stress levels to estimate reductions in permeability as a function of the void ratio (Vick, 1990).

Effective stress and void ratio are two factors that are associated to and directly influence permeability. As the confinement stress in the sample increases, the specimen becomes densified, and its volume of voids decreases. As the volume of voids decreases, the permeability in the sample decreases too, since the area through which the water flows decreases. There is a linear relationship between the void ratio and the effective stress applied to the tailing samples (Qiu and Sego, 2001), as well as between permeability and the effective stress in tailings (Ma et al., 2023). The vertical and horizontal samples tested show these linear relationships. As it can be seen in Figures 9(a) and 9(b), the tailings specimens tested presented void ratios of 1.5–0.56 in their loosest condition (σ′ = 19.6 kPa) and void ratios between 1.23 and 0.48 for the densest condition (σ ′ = 313.8 kPa). For both conditions, permeabilities ranging from 1 × 10⁻⁴ to 1 × 10⁻⁹ m/s were obtained.

With improvements in beneficiation technology, ores are finely ground, and the fines content of the tailings is increasing. Fine-grained tailings have low permeability, a long consolidation time, and a slow increase in strength, which implies high safety risks to the dams (Ma et al., 2023; Zhang et al., 2020).

Valenzuela (2015) presented results on saturated copper tailings from different mines in Chile and Peru. The most remarkable differences observed were in tailings with fines contents between 30% and 40%, probably because of a change in the soil fabric, since fines can occupy the spaces between the larger particles, thus decreasing the size of the voids as the size of the fines is reduced.

Figure 10 shows the k_v and k_h permeabilities obtained for tailings samples with fines contents between 12% and 100%, as well as the results and boundaries proposed by Valenzuela (2015). It is important to mention that these limits are exclusively for k_v.

Increasing the fines content in a tailings dam reduces permeability and jeopardises the stability of the dam (Singh et al., 2021; Saad, 2008). The effect of the fine content F_c on the permeability (k_v and k_h) for all test conditions, that is for the six stress increments (19.6, 39.2, 78.5, 156.9, 245.2, and 313.8 kPa), is shown in Figure 11, permeability in tailings samples tends to decrease as fines increase, regardless of the orientation of the test. The permeability in the vertical sample with the lowest fines content (F_c = 12.2%) is of about 1 × 10⁻⁵ m/s, while for the samples with the highest fines content (F_c = 100%), permeabilities of the order of 1 × 10⁻⁹ m/s were obtained. As for the horizontal samples, they showed a permeability of 1 × 10⁻⁵ m/s in the sample with a fines content of 18.3% and from 1 × 10⁻⁸ to 1 × 10⁻⁹cm/s for the specimen with fines content of 100%.

Due to the stratified nature of the tailings, differences were found in the fines content among samples trimmed either vertically or horizontally, extracted from the same Shelby tube. Because the amount of fines in adjacent samples of the same tube is not always equal, the term ‘difference in fines content’ (ΔF_c) was defined as follows:

where F_chs is the fines content in the horizontal sample, and F_cvs is the content of fines in the vertical sample.

Figure 12 shows the influence of the difference in fines content (ΔF_c) on the hydraulic anisotropy ratio (r_k). The hydraulic anisotropy ratio tends to increase when the fines content in the horizontal sample is lower than the fines content in the vertical sample, and the r_k value can be above 100. The opposite is the case when the fines content in the horizontal sample is greater than the fines content in the vertical sample; r_k decreases, and values of r_k less than unity may occur.

As already mentioned, in the literature, hydraulic anisotropy ratio values are found in tailings varying from 2 to 100. In the present study, for most of the samples tested, hydraulic anisotropy ratios were found in the intervals of 1 to 10; as shown in Figure 13, hydraulic anisotropy ratios above this range are due to a significant difference in fines content (ΔF_c > 10%) of the samples tested.

In this work, the results of 31 permeability tests (14 in a vertical direction and 17 in a horizontal direction) performed to evaluate the hydraulic anisotropy ratio r_k in undisturbed tailings samples were presented. The main findings of the research are summarised as follows:

• In the literature, it is possible to find various values of r_k for clays, sands, and rocks, but the results available for tailings are scarce. In this paper, the experimental procedure to obtain r_k in undisturbed tailings specimens subjected to permeability tests carried out on a constant head permeameter using the methodology of sample cutting in different directions has been presented. The samples were tested in a saturated state, because the test is non-destructive, six levels of effective stress equal to 19.6, 39.2, 78.5, 156.9, 245.2, and 313.8 kPa were applied to each specimen. For each stress, the vertical or horizontal permeability was obtained by applying hydraulic heads (h) of 150, 217, 284, and 350 cm of water column.

• The experimental method of cutting samples in different directions presented by Chapuis and Gill (1989) has been used to determine r_k in materials such as clays and rocks, but it is not known that this methodology has been used to determine r_k in tailings, which was implemented in this research.

• From the consolidation stage, the values of the C_c and C_v coefficients were obtained for the different samples tested. The influence of the fines content on C_c was evaluated; for samples with e ≤ 1, the C_c increases with the fines content from 0.056 to 0.102; for tailings samples with void ratios greater than unity, the C_c varies from 0.194 to 0.44.

• The effect of the void ratio and the fines content on the C_v coefficient was also evaluated; for tailings with fines contents less than 50%, C_v values of 2.6 × 10⁻² to 5 × 10⁻⁵ m²/s were obtained; while for tailings with fine content greater than 50%, C_v values of the order of 4.5 × 10⁻⁴ to 4.4 × 10⁻⁷ m²/s were obtained.

• In the experimental results presented in this work, it was shown that the fines content is a factor that has a significant influence on r_k. Therefore, because the tailings have a high stratification, it is recommended to obtain the F_c value of each of the specimens after determining k_v and k_h.

• Tailings were found to have a behavior similar to that described by Cubrinovski and Ishihara (2002) for mixtures of sand with fines. It was determined that the relationship of initial and final void ratios (e_i and e_f) tends to decrease as F_c increases in tailings samples with very low fines contents (between 0% and 30%); then, there is a transition zone in tailings with F_c ranging from 40% to 50%, in which e_i and e_f present their lowest value and begin to increase until reaching the highest values of void ratio for tailings with an F_c equal to 100%.

• The tailings studied with fines contents between 80% and 100% showed a significant variation in e_i and e_f (from 1.4 to 0.5); the void ratios exceeding unity belong to the most superficial samples tested. This is like what was found by Vick (1990), who pointed out that the highest void ratios are associated with tailing samples close to the surface of the dam.

• According to the literature, higher permeability favours high C_v values, while low permeabilities result in reduced C_v; the results obtained in this study show that for tailings with permeabilities between 1 × 10⁻⁴ and 1 × 10⁻⁶ m/s, C_v values vary from 9.4 × 10⁻³ to 4.05 × 10⁻³ m²/s, while in low permeability tailings, C_v values decrease to a range of 4.0 × 10⁻⁴ to 5.9 × 10⁻⁷ m²/s.

• The linear relationship between the void ratio and the effective stress applied in the tailings samples was verified, as well as that between permeability and effective stress; the tailings samples tested presented void ratios from 1.5 to 0.56 in their loosest condition (σ′ = 19.6 kPa) and void ratios between 1.23 and 0.48 for the densest condition (313.8 kPa). For both conditions, permeability values of the order of 1 × 10⁻⁴ to 1 × 10⁻⁹ m/s were determined.

• The permeability results as a function of the fines content were located within the boundaries established by Valenzuela (2015) for tailings with 15% and 30% fines content, and for tailings having from 40% to 100% of fines content.

• From the test results, it was determined that the permeability in the tailings samples tends to decrease as the fines content increases, regardless of the orientation of the test specimens. The permeability in the vertical specimen with the lowest fines content (F_c = 12.2%) was in the order of 1 × 10⁻⁵ m/s, while for the samples with the highest fines content (F_c = 100%) permeabilities obtained were in the order of 1 × 10⁻⁹ m/s. As for the horizontal samples, they presented a permeability of 1 × 10⁻⁵ m/s in the specimen with fines content of 18.3% and from 1 × 10⁻⁸ to 1 × 10⁻⁹ cm/s for the sample with fines content equal to 100%.

• The vertical and horizontal samples tested to evaluate r_k are from the same Shelby tube, but do not correspond to the same horizon; due to this and to the highly stratified nature of the tailings, in most of the tests, a difference in fines content was obtained between a vertical and a horizontal specimen. Therefore, the term difference in fines content (ΔF_c) was defined, representing the difference in the fines content of the horizontal sample and the fines content of the vertical specimen.

• It was observed that the hydraulic anisotropy ratio tends to increase when the fines content in the horizontal sample is smaller than the fines content in the vertical specimen, and the r_k value can exceed 100. The opposite case arises when the fines content in the horizontal sample is larger than the fines content in the vertical specimen; r_k decreases, and values of r_k less than unity may be found.

• Values of hydraulic anisotropy ratios, r_k, for tailings from 2 to 100 are found in the literature. In this study, for most of the samples tested, hydraulic anisotropy ratios were found to be in the range from 1 to 10; hydraulic anisotropy ratios above this range are due to a difference in fines content between samples (ΔF_c > 10%).

• Nowadays, the accuracy required in water flow models has been increasing, so it is necessary to determine realistic values of the hydraulic anisotropy ratio in tailings, such as those found in the present work, since the hydraulic anisotropy ratio within the tailings dam has an influence on aspects that can even affect the general stability of the dam.