1 Introduction

Tailings slurries are usually transported by pipeline systems to tailings dams where they are disposed. The coarse and fine fractions are usually separated, either by machinery before reaching the dam or by sedimentation in the dam, and their properties are usually very different. The fine fraction of iron ore tailings is often constituted by mixtures of silt-sized and clay-sized particles with little or no clay-minerals and exhibits a low plasticity (e.g., Morgenstern et al. 2016; Robertson et al. 2019).

Most of the literature on undrained strength is focused on sand tailings (e.g., Olson and Stark 2003; Idriss and Boulanger 2007; Sadrekarimi 2014; Reid 2019; Sadrekarimi and Riveros 2020; Ledesma et al. 2022) because they might be susceptible to liquefaction, and usually constitute the beach of the tailings dam which is the most important zone for stability analysis in upstream dams. On the other hand, studies of the characteristics and the strength of the plastic tailings are much rarer in the literature. However, they should not be disregarded since layers of plastic tailings are sometimes found in the midst of the sand tailings (Whittle et al. 2022; Becker et al. 2023). Moreover, the plastic tailings are very susceptible to undrained behavior, even when the rate of rise of the dam is relatively slow (Vick 1990; Mittal and Morgenstern 1976) since their coefficients of consolidation are typically much lower than the sand tailings.

Mac Iver (1961), Penna (2007), Penna (2008) and Ferreira (2016) found low values of the su/σ′v (ratio between undrained strength and vertical effective stress) of plastic tailings in good agreement with two classical correlations between undrained strength and plasticity index (PI): su/σ′v = 0.11 + 0.0037·PI (Skempton 1957), and su/σ′v = 0.045·PI 0.5 (Bjerrum and Simons 1960). On the other hand, these values are significantly lower than other correlations for clays (e.g., Mesri 1975) that are sometimes used for plastic tailings (e.g., Whittle et al. 2022), and the peak su/σ′v of sand tailings (e.g., Olson and Stark 2003; Sadrekarimi 2014).

The objective of the present work is to study the distribution of the normalized undrained strength of the plastic tailings found in the Germano dam in Mariana, Brazil using the results currently in the public domain (Morgesntern et al. 2016). It will be shown herein that the undrained strength of plastic tailings may be significantly lower than the sand tailings.

2 Iron ore plastic tailings

The iron ore plastic tailings found in Brazilian dams usually have a reddish color and a low plasticity index. They are composed of silt-sized and clay-sized particles, and the content of clay minerals is very low or null (Morgenstern et al. 2016; Robertson et al. 2019). The presence of iron oxides results in a high density of solids (Gs) that may exceed 4.0. Despite clay minerals are almost entirely absent, the plastic tailings found in the Germano dam have low hydraulic conductivity and are classified as low plasticity clay due to their particle size and Atterberg limits (Morgenstern et al. 2016).

According to Vick (1992), Mac Iver (1961) was a pioneer of the investigation of the undrained strength (su) of plastic tailings. More recently, Penna (2007), Penna (2008), Ferreira (2016) and Morgenstern et al. (2016) presented undrained strength results of the iron ore plastic tailings from the Germano dam. They found su/σʹv ranging from 0.09 to 0.22. Table 1 presents characteristics of plastics tailings studied by several authors.

Table 1 Geotechnical characteristics of plastic tailings
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2.1 Undrained strength of iron ore plastic tailings based on CPTu and FV tests

The corrected cone resistance (qt) may be used to estimate the undrained strength of clays:

$${s}_{u}=\frac{{q}_{t}-{\sigma }_{v}}{{N}_{kt}}$$
(1)

The cone factor Nkt may be determined by comparing the results of piezocone and field vane tests (CPTu and FV, respectively). In natural clays, Nkt typically varies from 10 to 18 (Robertson and Cabal 2015). Bedin (2006) found Nkt ranging from 12 to 19 in Bauxite tailings. Ferreira (2016) analyzed three CPTu and one FV tests in plastic tailings from the Germano dam and reported Nkt = 18, on average.

Several factors may influence the undrained strength measured by FV tests (rate of shear, anisotropy time effects etc.). The combination of these factors requires that the undrained strength obtained by the field vane (su,FV) be corrected for the use in geotechnical design (su,d):

$$s_{u,d} = \mu \cdot s_{u,FV}$$
(2)

The empirical correction factor (μ) is related to the plasticity index of the soil and may be estimated by back-analysis of known failures (Bjerrum 1973; Azzouz et al. 1983).

3 Studied material

The plastic tailings studied in this research belong to the reservoir of the Germano dam located in the town of Mariana, Minas Gerais state, Brazil. Figure 1 shows the area where these tailings are deposited.

Fig. 1
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Satellite photo taken in 2015 of the reservoir of the Germano dam (adapted from Google Earth 2023)

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According to Morgenstern et al. (2016), the plastic tailings from the Germano dam are composed entirely by silt and clay-sized particles, have low plasticity (PI = 7%–11%) and low permeability (k < 10–8 m/s).

4 Methodology

The results of the CPTu and FV tests (ASTM 2020, and ABNT 1989, respectively) performed in 2014, 2015 and 2016, presented by Morgenstern et al. (2016), were used in this study.

Since these data were not provided in electronic spreadsheet form, the first step was to use a software to digitalize and automatically collect the data from the graphs of tip resistance (qt), friction ratio (Rf) and porepressure (u2) at 0.02 m intervals. The undrained strength (su) was obtained in the same manner from the FV tests results.

4.1 Criterion for identification of plastic tailings based on CPTu tests

Sampling of tailings presents several difficulties (Milonas 2006) and CPTu tests are usually used for identification of the tailings type and estimation of geotechnical properties.

Plastic tailings and natural, normally consolidated clays of the same plasticity index show similar compressibility and coefficient of consolidation (Penna 2007; Vick 1992). The presence of clays may be identified in CPTu tests because they exhibit low values of cone penetration resistance (qc) and high excess porepressure during the cone penetration (Campanella et al. 1984). Lima (2006) compared CPTu tests performed in the Germano dam with deformed samples of the same depth and concluded the plastic tailings show a similar behavior to the natural clays.

Robertson (2009, 2016) proposed a criterion for the identification of “clay-like materials” based on the Soil Behavior Classification Index Ic > 2,60 (zones 1, 2, 3 and 4 of the SBTn chart—“Soil Behavior Type Normalized”).

There are some questions about the reliability of the SBTn abacus, especially in the case of stratified soils, as it is based on Sleeve Friction (fs). There is a lack of accuracy in fs measurements because of the pore pressure effects on the ends of the sleeve, tolerance in dimensions between the cone and the sleeve, surface roughness of the sleeve and load cell design and calibration (Lunne and Andersen 2007). However, according to Robertson (2009) this index is mainly controlled by the Corrected Tip Resistance (qt) in soft soils, which would be more accurate.

The definition of a criterion for the identification of the plastic tailings began with a meticulous analysis of the CPTu results in the “pure slimes” region identified by Morgenstern et al. (2016). In this region, a CPTu test (GSCPT16-05) and a FV test (GSVST16-02) were performed. Several disturbed samples were collected from borings GSSAM16-02 and GSSAM16-02B, few meters away from the CPTu and FV tests. Figure 2 presents photos of these samples. All the hallmark characteristics of plastic iron tailings were identified in these samples: plasticity, high fines content and a reddish color.

Fig. 2
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Disturbed samples from various depths in the region of “pure slimes”–boring GSSAM16-02 (Morgenstern et al. 2016)

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Figure 3 presents the results of the CPTu test GSCPT16-05 that was performed close to the boring GSSAM16-02. The behavior of the soil close to the surface is typical of sands, and the nearby boring revealed gray sand tailings up to the elevation 914 m. At elevations 898.2 m and below 886 m (close to the bottom of the reservoir), qt and Rf increase sharply while u2 decreases, and Ic < 2.60, indicating these layers are composed of mixtures of sand and silt tailings. In most of the profile, however, the tip resistance was much lower and increased linearly with depth. The friction ratio was also low, between 0 and 2%, high values of positive excess pore pressure developed during the cone penetration, and Ic > 2.95. This is the behavior pattern expected from clayey soils.

Fig. 3
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CPTu test GSCPT16-05 (adapted from Morgenstern et al. 2016)

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Lima (2006) analyzed the formation of a deposit of fine mining tailings in other location of the Germano dam by studying CPTu tests and collecting disturbed samples and identified a similar behavior (Fig. 4). Between elevations 893 m and 895 m, Ic > 2.95, qt decreases sharply and u2, which previously coincided with the hydrostatic line, showed a significant positive excess. At this elevation the disturbed samples revealed a layer of fine, plastic tailings.

Fig. 4
figure 4

CPTu performed at the Germano dam (adapted from Lima 2006)

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Thus, the criterion adopted in this work for the identification of plastic tailings layers are Ic > 2.95, and positive excess pore pressure. In general, these conditions correspond to low values of tip resistance (in the aforementioned cases, qt < 1 MPa). It is worth mentioning that the equilibrium pore pressure has an important influence on Ic as will be discussed in detail later.

5 Interpretation of results

5.1 Groundwater level interpretation

As the CPTu tests were carefully analyzed, it became evident that a few of the initial pore pressures (u0) adopted by Morgenstern et al. (2016) should be reinterpreted since they have a great influence on Ic and su/σ′v. In this work, the groundwater level (GWL) identified in the piezocone tests and the available dissipation tests were considered for the calculation of u0, according to the following method. Since most of the CPTu tests had no dissipation tests or piezometers nearby, the GWL position was frequently based on the u2 graph in the sand layers.

5.2 Perched water tables

In Fig. 5, Ic > 2.95, low qt and positive excess pore pressure indicate two important plastic tailings layers: the upper between elevations 896.5 m and 897.5 m, and the lower between at 892 m and 893 m. Above these layers, Ic, qt and the absence of excess porepressure indicate the presence of sand tailings. Two GWL are perched on the upper and lower plastic layers. The first GWL is at elevation 904.5 m and the second is at 896.0 m. The solid lines fitted to the pore pressure graph in Fig. 5 have a gradient of 9.81 kPa/m and fit very well to the perched water tables, indicating the plastic layers have a significant lateral extension. It should be noted that, if the porepressure below 896 m was inadvertently estimated based on the upper perched GWL (dashed line), u0 and σ′v would be overestimated and underestimated by approximately 80 kPa, respectively.

Fig. 5
figure 5

Interpretation of the pore pressure in CPTu test F40/98 (adapted from Morgenstern et al. 2016)

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5.3 Vertical downward flow

In the CPTu test GSCPT16-05 (Fig. 3), dissipation tests were carried out at different depths. The circles indicate three dissipation tests that reached equilibrium. The other tests did not reach equilibrium. The GWL is at elevation 914 m. The dashed line indicates a hydrostatic pore pressure distribution, and the continuous line shows the interpretation based on the dissipation tests. Clearly, the actual pore pressure is much lower than the hydrostatic value because there is a vertical downward flow towards the sand tailings layer on the bottom of the reservoir. In this case, if one uses the hydrostatic line, the pore pressure and the su/σ′v ratio would be overestimated.

5.4 Determination of N kt

Morgenstern et al. (2016) presented 405 FV tests. However, many of these tests were performed in layers identified as sand tailings or in layers of plastic tailings that were very close to the overlying or underlying sand tailings layers.

To ensure that the Cone Factor Nkt values are solely representative of the plastic tailings and not influenced by the sand layers, the FV tests performed in sandy layers, in plastic layers with thickness < 13 cm, and in plastic tailings at a distance of less than 13 cm from the upper or lower sand layers were disregarded (the last two criteria consider a typical Vane height of 13 cm). After the adoption of these criteria, 70 FV tests remained. These tests were conducted in close proximity to 16 CPTu tests (Table 2).

Table 2 Nkt values for FV tests performed in plastic tailings
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The average values of σv and qt along the height of the Vane are considered. The unit weight of the tailings from the Germano dam was equal to 22 kN/m3 (Morgenstern et al. 2016). In this study, the undrained streght measured by the Vane test (su,FV) was not corrected since PI of the plastic tailings is between 7 and 11%, corresponding to the average correction factor µ of 1.1 according to Bjerrum (1973) or 0.98 according to Azzouz et al. (1983). Table 2 shows the Nkt values for each FV test.

Typically, Nkt ranges from 10 to 18 for natural soils (Robertson and Cabal 2015). Bedin (2006) found Nkt values from 12 to 19 for bauxite tailings and Ferreira (2016) analyzed 12 FV tests close to the CPTu test F48/89 and obtained an average Nkt value of 18 for the plastic tailings from the Germano Dam.

Table 2 shows some values that are quite extreme and different from those in the literature. The Inter-Quartile Range method was used to detect the outliers. Q1 is the first quartile of the data, i.e., 25% of the data lies between the minimum and Q1. Q3 is the third quartile, i.e., 75% of the data lies between the Q3 and the minimum. Since the inter-quartile range (Q3–Q1) is not sensitive to the distorting effect of extreme scores (Witte and Witte 2017), the values below Q1–1.5(Q3–Q1) or above Q3 + 1.5(Q3–Q1) were ignored to avoid skewing the estimation of the undrained strength. This criterion excluded three measurements: Nkt = 54.6, 66.1 and 153.2.

Figure 6 presents the histogram of the remaining 67 values of Nkt. The Nkt values are best represented by a triangular or a lognormal distribution. In this study the triangular distribution (red lines) was used because of its simplicity.

Fig. 6
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Histogram and triangular distribution of Nkt

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Using the mean, the median or the mode of Nkt would result in different probabilities of underestimating or overestimating the value of su. In a right-skewed distribution like Fig. 6, Mode < Median < Mean. The mode (Nkt = 16.20) is the most likely value, but its use would cause a higher probability of overestimating su, as approximately 66% of the Nkt values are greater than the mode. On the other hand, using the mean (Nkt = 20.06) would also introduce bias in the su estimation since 45% of the Nkt values are greater than the mean. Therefore, the median of the distribution (Nkt = 19.37) was used since it does not introduce bias in the estimation of su.

5.5 s u/σʹ v calculations

According to the criterion outlined before, layers of plastic tailings were identified in 31 of the 75 CPTu tests presented by Morgenstern et al. (2016). The su/σʹv ratio was determined at every 0.02 m, using Eq. 1 and the median of Nkt, for all layers of plastic tailings present in these 31 CPTu tests.

The undrained strength of the plastic tailings close to the boundaries with sand tailings was consistently higher than the su in the middle of the layers. Ahmadi and Robertson (2011) performed numerical analysis to simulate the CPTu test in soils with interspersed layers of sand and clay with different thicknesses. Like Lunne et al. (1997), they observed that the materials above and below a given soil layer influence the value of qt. In soft clay layers, the influence of overlying and underlying sand layers is limited to a zone of approximately 2 cone diameters from the boundaries, which corresponds to 0.05 m. As a result, qt of clay layers with thickness of less than 0.10 m is unreliable, as well as the qt values in the first and last 0.05 m of a thicker clay layer. In the present work, it was decided to ignore the first two and the last two measurements of each plastic tailings layer since qt measurements were collected at 0.02 m intervals.

Moreover, su values were grouped in three categories to assess the influence of the layer thickness (t): thin (t ≤ 0.5 m), intermediate (0.5 m < t ≤ 1.0 m), and thick layers (t > 1.0 m). Five scenarios were considered:

  1. 1.

    All su values of the plastic layers were considered.

  2. 2.

    All su values taken at distances of less than 0.05 m from the sand boundary were disregarded.

    1. 2.1

      Thin layers: only layers with t ≤ 0.5 m are considered and each layer is represented by its average,

    2. 2.2

      Intermediate layers: only layers with 0.5 m < t ≤ 1.0 m are considered and each layer is represented by its average, and

    3. 2.3

      Thick layers: only layers with (t > 1.0 m) are considered and each layer is represented by its average.

Figure 7 presents the histogram (blue bars) and the lognormal probability distribution (orange line) of su/σ′v for all plastic tailings layers. Figure 8 presents the histogram and the lognormal probability distribution of su/σ′v values, discarding CPTu measurements taken at distances of less than 0.05 m from the sand boundary.

Fig. 7
figure 7

Histogram and lognormal distribution for all layers of plastic tailings based on the Nkt median (n = 17,900)

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Fig. 8
figure 8

Histogram and lognormal distribution for all layers of plastic tailings based on the Nkt median, discarding CPTu measurements taken at distances of less than 0.05 m from the sand boundary (n = 13,934)

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Discarding the su/σ′v values close to the borders of the plastic tailings layers led to a significant reduction in mean and median. The discarded measurements at the borders were higher than the values in the middle of the layers, probably due to the influence of the adjacent sandy layers. The change in the mode was small since the most common values were only slightly influenced by the discard of CPTu measurements. The standard deviation and the coefficient of variation decreased to a lesser extent.

It should be noted that the histograms in Figs. 9 and 10 show a deviation from the lognormal probability function, caused by an overrepresentation of the thick layers in the sample, since they have a much larger number of CPTu measurements. For example, CPTu test GSCPT16-05 has a 15.18 m thick layer of plastic tailings with a mean su/σ′v of 0.050. Since measurements are taken at every 0.02 m, this corresponds to 759 measurements (i.e., 5.4% of all data). Representing each plastic tailings layer by the mean value of its su/σ′v measurements eliminates this distortion and leads to a much better agreement between the histogram and the lognormal distribution (Fig. 9).

Fig. 9
figure 9

Histogram and lognormal distribution for all layers of plastic tailings based on the Nkt median, discarding CPTu measurements taken at distances of less than 0.05 m from the sand boundary and representing each layer by its average value (n = 845)

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Fig. 10
figure 10

Histogram and lognormal distribution for thin layers of plastic tailings based on the Nkt median, discarding CPTu measurements taken at distances of less than 0.05 m from the sand boundary and representing each layer by its average value (n = 693)

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To evaluate the influence of the layer thickness on su/σ′v, a new analysis was performed. Each layer was represented by its su/σ′v average and the data were divided in thin layers (t ≤ 0.5 m), intermediate layers (0.5 m < t ≤ 1.0 m), and thick layers (t > 1.0 m) are considered, and each layer is represented by its average.

693 layers of plastic tailings with a thickness of up to 0.5 m (thin layers) were found. As the boundary values have already been discarded, layers with thicknesses of less than 0.1 m are not present. Figure 10 presents the histogram with the lognormal distribution for thin layers. Mean, median, and mode were slightly higher than those found when all layer thicknesses were evaluated together. This result demonstrates that the thinnest layers present higher su/σ′v values than the other layers.

99 intermediate layers of plastic tailings were found (0.5 m < t ≤ 1.0 m). Figure 11 presents the histogram with the lognormal probability distribution. Unlike thin layers, intermediate layers have mean, median, mode, and standard deviation lower than the distribution with data from all layers. This result is consistent with the previous observation that thin layers have higher su/σ′v values than thicker layers.

Fig. 11
figure 11

Histogram and lognormal distribution for intermediate layers of plastic tailings based on the Nkt median, discarding CPTu measurements taken at distances of less than 0.05 m from the sand boundary and representing each layer by its average value (n = 99)

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53 thick layers of plastic tailings were found (t > 1.0 m). Figure 12 presents the histogram with the lognormal probability distribution. Mean, median and mode were significantly lower than those found for the thin and intermediate layers, confirming that the thicker the layer, the lower the su/σ′v values.

Fig. 12
figure 12

Histogram and lognormal distribution for thick layers of plastic tailings based on the Nkt median, discarding CPTu measurements taken at distances of less than 0.05 m from the sand boundary and representing each layer by its average value (n = 53)

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Furthermore, it should be noted that the ratio between the standard deviation and the mean (coefficient of variation, CV) of thin and intermediate layers is similar and significantly higher than thick layers (CV = 40%, 47%, and 29% for thin, intermediate, and thick layers, respectively). In other words, the strength of thick layers is more homogeneous.

Figure 13 confirms that, as the layer thickness increases, su/σ′v decreases and becomes more homogeneous. Three possible explanations were devised for this phenomenon:

  1. a)

    The upper and lower sand layers may influence a zone larger than 2 cone diameters in the plastic layer. The thinner the plastic layer, the more important would be this effect. On the other hand, in thick layers this effect would be negligible. The sparse evidence in the literature does not seem to support this explanation.

  2. b)

    The consolidation processes of the thicker layers would be incomplete, and their actual effective stress would be lower than the assumed value, resulting in reduced values of su and su/σ′v. However, it seems that this is not the case, because the su/σ′v ratio is approximately constant with depth within a given layer, even in the thickest layers. This is not compatible with a situation of ongoing consolidation since the degree of consolidation should be minimum in the middle of the layers and 100% close to the boundaries.

  3. c)

    The more likely explanation seems to be associated with the grain size. Although all layers are composed of plastic tailings, their grain size may vary, leading to differences in strength. The grain size of the thick layers may be finer because they may be farther from the discharge points, resulting in lower undrained strength.

Fig. 13
figure 13

Relation between su/σ′v and layer thickness for 845 layers of plastic tailings

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Table 3 presents a summary of the values obtained for su/σ′v for plastic tailings. It is worth noting the low strength of these plastic tailings. For example, the mode was below 0.19 in all cases. In the case of layers with thickness of more than 0.5 m, the median is below 0.15 i.e., the chance of su/σ′v < 0.15 is 50% or more.

Table 3 Summary of su/σ′v in the various analysis based on the median Nkt
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6 Concluding remarks

The coefficient of consolidation of plastic tailings is much lower than the sand tailings’. Despite this, the literature about undrained strength of plastic tailings is rarer.

In this research, after comparing disturbed samples of plastic tailings with CPTu tests, an identification criterion was devised, based on Ic > 2.95 ​​(Robertson 2009; 2016) and positive excess pore pressure.

After screening for plastic tailings, 31 CPTu and 70 FV tests were analyzed and compared, resulting in a total of 67 Nkt estimates. An asymmetrical distribution was found, and the median (Nkt = 19.37) was chosen to avoid introducing bias in the su estimations. Perched water tables and downward flows were considered when analyzing the pore pressure of each CPTu test, and the qt measurements taken from plastic tailings at less than 2 cone diameters away from the neighboring sand tailings were ignored to minimize the influence of the sand layers below and above the plastic layer.

It was found that the thinner a layer of plastic tailings was, the higher was its normalized undrained strength, possibly due to variations in particle size or influence from neighboring sand layers. Moreover, the strength of the thicker layers is more homogeneous. Lognormal distributions fit very well the histograms. The mode, median, and mean of su/σ′v from layers with thickness of 0.5 m or less were 0.182, 0.207 and 0.223, respectively. For layers with thickness of more than 1.0 m, these parameters were 0.097, 0.107 and 0.110. It should be highlighted that these values are significantly inferior to the peak normalized undrained strength of sand tailings (for example, su/σ′v0 > 0.205 according to Olson and Stark 2003). Despite this, it is relatively common to use the same set of undrained strength parameters for representing interspersed layers of plastic and sand tailings in stability analysis (Carrier 1991; Morgenstern et al. 2016; Robertson et al. 2019; Sadrekarimi and Riveros 2020). This consideration does not seem appropriate to the plastic tailings of Germano dam since their normalized undrained strength is significantly lower than the sand tailings.