Simulation of tailings release in dam break scenarios using physical models

This article presents an experimental study performed to evaluate the volume of material released from the reservoir during a tailings dam failure event using models. To verify the influence of the parameters related to the breach geometry and the undrained shear strength (Su) in a failure event, 20 scenarios were simulated considering the absence of water in the reservoir. The material used to simulate tailings was bentonite, due to the similarity between the properties of the mud and mineral tailings sludge. Geometry and undrained shear strength were adjusted considering a scale factor of 1: 500. Regarding the studied parameters, the geometry of the breach was based on data from literature, whose lateral slopes were 0.50 H: 1V, 0.51 H: 1V and 0.5467 H: 1V in the trapezoidal breaches and 1: 1 (L / H = 0.97) and 1: 1 (L / H = 1.1) in the rectangular ones. The undrained shear strength ranged from 0.030 to 0.20 kPa. The results allowed to conclude that the mobilization of material increases with the average aperture width of the trapezoidal breach, being this the distinct behavior in rectangular breaches. Although the rectangular breaches had smaller average widths compared to the trapezoidal breaches, their base widths were larger and it is possible to infer that the mobilized volume depends on the geometry and the average width of the breach.


Introduction
The mining activity generates millions of cubic meters of materials extracted and handled in the beneficiation process each year. In the case of tailings, the produced amount depends on the used process for extraction, the ore concentration and the deposit location. The quantification of this material is complex, due the diversity of operations and technologies used in the extraction and processing technics. According to Portal Brasil (2014), during 2013 in Brazil, the share of mineral goods in exports was 23.5 %. In the GDP (Gross Domestic Product) of the mineral sector, which was U$ 85 billion, the mineral assets represented participation of around 4% in the national GDP.
Among the alternatives for disposing tailings, miners frequently have chosen to construct dams and store tailings in their reservoirs. However, if the dams are inadequately built or designed, these structures represent a great risk to society, to the environment and to the economy. Generally, these materials raise uncertainties regarding their mechanical behavior, either due to the low shear strength or the variable permeability. Therefore, continuous monitoring of the material throughout the construction and operational process is necessary.
For water retention dams, the dam break evaluations are performed using the hydrodynamic approach, whose focus is on understanding the potential effect of flooding through parameters such as velocities and maximum discharges. However, this approach is inappropriate for tailings dams, due to the existence of physical properties other than the upstream material compared to water reservoirs, so it is necessary to understand the mass mobilization behavior of the mineral tailings using a geotechnical approach, which is a more realistic assessment of the phenomenon.
The objective of this research was to develop a theoretical / empirical study to evaluate the released volume of tailings in dam failure scenarios using bentonite as the contained material to simulate the conventional mineral tailings.
The tailing dams (See Figure 1) represent artificial retention barriers for containing mineral waste from ore beneficiation. In general, these structures are commonly initiated by constructing a starting dam with mining waste, tailings or compacted soil. Once the structure is constructed, the pulp is released in the upstream side of the dam by pumping the tailings according to the beneficiation technics of the ore. The tailings are hydraulically deposited from the crest of the starting dike, to form a tailings beach. Currently three constructive methods are highlighted: upstream method; downstream method; centerline method. Besides these, there is the mixed method that represents the mixture between the traditional methods of construction.

Figure 1
Fundão dam in 2015 in the municipality of Mariana-MG. Source: Minning (2018) According to ANA (2017), there are 839 tailings dams in Brazil, representing 3.66 % of dams worldwide. These dams are mainly susceptible to slope instabilities, overtopping, and earthquakes (ICOLD, 2001). Rico et al. (2008) cited that 83 % of failures occurred in inactive dams, 15 % in active dams and two percent occurred in inactive but maintained dams. In addition, in the same studies, 55.9 % of the incidents occurred in dams with more than 15 m depth and 22.6 % in dams with 30 m. Azam and Li (2010) carried out a study with 18,401 mine sites. They observed that the failure rate in the last 100 years was estimated at 1.2 % and this is about twice the magnitude of failure rate of conventional water retention dams. In addition, they realized that climatic factors, poor management of these structures and flow were the factors that generated most failures in these structures. The results obtained in this study are similar to those reported in literature. Figure 2 illustrates an example of failure of the Marriepsruit dam in the suburb of Virginia in South Africa caused by the rains in the region. Davies (2002) cited a worldwide inventory of 3,500 known tailings dams in the last 30 years (1970 to 2001) of two to five faults per year, which is equivalent to an annual probability between one in 700 and one in 1750. This failure rate does not provide a favorable comparison with less than one in 10,000 that appears to represent conventional dams.

Materials and methods
For the research presented herein, the material used in substitution for the tailings was bentonite due to its strength and rheological characteristics being similar to mineral tailings whose physical characteristics are presented in Table 1. Regarding the reading equipment (see Figure 3) of the post-rupture relief, it consists of: a) computer with MyCam ® software; b) simulator box with cracks in wood; c) metal structure as a base for the reading support with fixed and movable planks; d) five Megapixels webcam with 640 x 480 image resolution; and e) linear scanning laser.
The simulation box was designed with the geometry of 40 cm x 50 cm x 60 cm (width, length and height) being filled up to 15 cm in height relative to the base of the same to simulate a tailings dam scale 1: 500, i.e. with a height of 75 m, without water. To define the lateral slope walls adopted in the study, the researches of MacDonald and Langridge-Monopolis (1984), by Froelich (2008) and Brunner (2014) were considered. According to MacDonald and Langridge (1984), the breach has a trapezoidal shape with lateral slopes of 0.5 H: 1V, whereas Froelich (2008) cited that the lateral slope of breaches opened by a piping mechanism is 0.7 H: 1V. Brunner (2014) stated based on FERC notes that dross and tailings dams reach 1: 1 or 2: 1 lateral slopes. In this manner, lateral wall slopes of breaches of 0.50 H: 1V, 0.51 H: 1V, 0.5467 H: 1V and 1H: 1V were adopted. Additional information of breaches is shown in Table 2.  Table 2 Geometry of rupture breaches adopted.
In order to understand the behavior of the released volume, the technique of topographic survey using the laser triangulation method was used. With this technique, as there are variations of material shape during the failure process, the laser scanner, which is kept in fixed conditions (focal distance and base distance), allows to evaluate the surface by reading the object through equidistant photographs. By this way, variations of the altimetric dimensions are obtained, at each cross section, by tortuosity (curved formations) or by interruption of lines (rectilinear formats).
Given the distance where the laser is incident to the object and the reflected signal of the object, the images are captured by the webcam and depending on the difference between the capture times, the 3D image is drawn. Once the surface has been generated after the stipulated time, the sectional registration procedures of the surface generated begins. The coordinates of the points are calculated from Equations (1), (2) and (3). Where: DH -Horizontal distance measured directly by the sliding plate in the direction of the larger dimension of the simulator box, in centimeters; ρ pixel / cm -Density of pixels, i.e. pixels per unit length for different altimetric dimensions, in pixels/cm; f (L,C) -2D coordinates of the pixels according to the rows and columns of the image, in centimeters.
The Y-coordinate was obtained for every centimeter during the generation of photographs using a scale coupled to a sliding board. Once the photographs were taken from the moment of rupture, these images were grouped in a program developed in MatLab ® software, which allowed the generation of the X and Z coordinates from the chromatic identification of the laser referring to the red tone present in the generated images. In this way, a cloud of points (around 8000 to 10000 points) was produced, which materializes the three-dimensional surfaces when integrated with SURFER 3D ® software, subsidizing geostatistical interpolation by the kriging method offered by the Map tool in the "contour map" option and in turn creating the contour maps (See Figure 4). For 3D surface modeling, the surface option was used and the wedge shape was interpreted as a function of the breach geometry and the values of S U .

Figure 4
Failure wedge level curves.
In order to obtain the undrained shear strength (S u ) of the bentonite in function of the variation of the moisture content of the liquefied material, box L was used. The equipment was built in acrylic to facilitate the measurement of the horizontal distances from the visualization of the deposition of the sides of the carton, as shown in Figure 5a and 5b.  The moisture content of the bentonite was changed and the undrained shear strength (S u ) was calculated based on the modified infinite slope method (see Equa-tion 4), and then validated by the tailings scattering studies of Lazarim (2015). The undrained shear strength (S u ) is calculated as a function of the soil deposition angle after the opening of the L-box breach, the specific weight of the loose material (γ) and the average height of the deposited material (h average ). S u = γ. h average . cos²a . tga Where: S u : undrained shear strength of the material; a: tailings deposition angle; γ: Specific weight of the material; h average : average height of the material. The bulk unit weight of the mate-rial (γ) was obtained by filling in a 5 x 5 x 10 cm box in a loose state and then weighed using a precision scale, whose value was calculated as a function of the soil weight ratio (P soil ) and the volume of the box (V soil ). To calculate the mobilized volume of material from the reservoir, the method of equidistant surfaces or method of the average areas was adopted. This method calculates the volume of material between extreme areas delimited by the level curves, according to Equation 5: .
Where: V mob. -Calculated mobilized volume of material; A top -Area delimited by the top level curve; A base -Area delimited by the base level curve; E -Vertical distance between base and top levels (15 cm).
The top area was generated from the interpolation of the lengths obtained by the average slope of the physical model (a) of each section in the plane referring to the dimension of 15 cm, referenced by the base of the simulation box from the base area.
When the small-scale models are submitted to the non-centrifuged tests (as in presented study), a scale factor must be applied to the material or equipment characteristics in order to the test corresponds to the prototype. Table 3 lists the scale factors for several parameters, based on the similarity theory. The aspects considered from the similarity theory are similar to those presented in the study by Dell 'Avanzi et al. (2006) , Lazarim (2015), Silva (2013) andSouza Junior et al. (2017).

Parameters and properties Scale Factor (Prototype / small-scale model)
Gravity 1 Length λ
The calculation of the parameters of mass releasing in real scale, is based on the quantities on Table 3. Therefore, the variables of the physical model are converted into prototype values from Equations (6), (7) and (8): Where: λ -Scale factor; H -Height of the dam; S u -Undrained shear strength; V -Volume of released material.

Discussion
Several difficulties occurred during the tests for granulometric characterization of sodium montmorillonite. In the study herein presented, the authors preferred to present the granulometric distribution curve obtained in tests performed without deflocculant ( Figure 6), using the laser granulometry measurement technic. The obtained distribution of granulometric fractions of bentonite is: 89.84% of silt, 8.25% of sand and 1.91% of clay. Certainly, those values correspond to the flocculated grains of bentonite. The classification was generated from the standard NBR 6502 (ABNT, 1995), whose applicable material designation is silt with little sand and traces of clay. This bentonite presents a plasticity index (IP) of higher than 15%, characterizing a material of high plasticity.
Regarding the undrained shear strength (S u ), that were obtained using the L box test procedures, as previously described, it was adapted a moisture content range from 890 % to 970 %, referring to the range of undrained shear strength (S u ) of 0.030 to 0.20 kPa, as shown in Figure 7. Such values of undrained shear strengths are compatible with those discussed by Olson and Stark (2002) and with the scale 1:500, adopted for the physical model. Olson and Stark (2002) presented a study showing that the undrained shear strength ratio of normally consolidated tailings, S u /σʹ vo , ranges from 0.04 to 0.20, in pre-failure conditions. It represents values of Su ranging between 0 and 105 kPa in the field and between 0 and 0.21 kPa in the small scale model. After the tailings dam failure, the shear strengths is referred to as liquefied undrained shear strength, with values normally ranging between 1 and 17 kPa, as discussed in Lucia (1984).
Using the technique of obtaining undrained shear strength (S u ) as a function of the moisture content (w%) in slurry consistency, it was verified that, as the moisture content of the bentonite was increased, the deposition angles of the material decreased and consequently reduced the Su value of the material.
The relationship between the undrained shear strength (S u ) and the volume released from the reservoir (V.lib) can be seen in Figure 8. One can note that as the average width of the breach (Lm) increases, a greater volume of bentonite is mobilized during the tests. Comparing the breach formats, it is possible to notice that the breach geometry influences the mass mobilization. Although the rectangular and trapezoidal breaches allowed the formation of similar wedges, the average widths of the rectangular breaches were smaller, and the values of mobilized mass were superior to the trapezoidal breaches.
Probably, since the measurements of the base widths of the rectangular breaches were greater than the base widths of the trapezoidal breaches, the magnitude of the mobilized mass can be significantly influenced by the size of the breach base. In the breaches with slopes 0:50 H: 1 V, 0.51: 1 V and 0: 55 H: 1 V, it was noticed that the greater the increase in the average width of the aperture, the greater the mass mobilized.
As for the rectangular breaches B4 and B5, it was noticed that there was a reduction of mobilized mass with the increase of the breach width. In general, in the B5 simulations, the mobilized volumes values were smaller than those on a shorter breach (B4). Possibly, this behavior can be justified by the variation of strains generated after opening the breach. The stress relief generated after formation of the breach allowed the formation of wedges with smaller widths and larger lengths, caused by the stabilization of the slopes of the central sections (S2, S3 and S4) at smaller angles in the breach B5 with respect to the breach B4.

Figure 8
Results of the post-rupture mobilized mass evaluation of the physical model of tailings reservoir.

Figure 9
Comparison of the mobilization of material mass as a function of the undrainedshear strength (S u ) in breach B1.
With respect to the shape of the wedge in the B1 breach, it was noted that when the undrained shear strength (S u ) value reduces, the slopes of the sections reduce as well. In addition, the base height of the deposited material immediately near the breach point increases, as there is an increase in un-drained shear strength (S u ), according to Figure 9. This implies that the more rigid the material, the more superficial the mobilized material.
As can be seen in Figure 10, in two breaches (B3 and B4) with different geometries and using material with different undrained shear strengths, different wedge formats were obtained. In breach 4 (trapezoidal format), the formation of ellipsoidal wedges was observed, which was not observed in breach 3 (rectangular format) that generated wedges with circular shapes. The angles of section S1 and S5 were steeper for breach 3 compared to breach 4, while sections S2, S3 and S4 presented angles with close values.

Figure 10
Comparison of the mobilization of material mass as a function of the breach geometry.