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Article

Spatial and Temporal Analysis of Surface Displacements for Tailings Storage Facility Stability Assessment

by
Wioletta Koperska
1,
Paweł Stefaniak
1,
Maria Stachowiak
1,
Sergii Anufriiev
1,*,
Ioannis Kakogiannos
2 and
Francisco Hernández-Ramírez
2
1
KGHM Cuprum Ltd.—Research and Development Centre, Gen. W. Sikorskiego Street 2-8, 53-659 Wrocław, Poland
2
Worldsensing—Viriat 47, 10th Floor, 08014 Barcelona, Spain
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(22), 10715; https://doi.org/10.3390/app142210715
Submission received: 23 September 2024 / Revised: 31 October 2024 / Accepted: 8 November 2024 / Published: 19 November 2024
(This article belongs to the Special Issue Automation and Digitization in Industry: Advances and Applications)
Browse Figures
Figure 1
<p>Countries with the highest number of TSF dam failures (in the period 1915–2019).</p> "> Figure 2
<p>Sample Moran scatterplot.</p> "> Figure 3
<p>Moran scatterplot for displacement velocity (<b>a</b>) and displacement acceleration (<b>b</b>).</p> "> Figure 4
<p>Hot spot analysis result for velocity and acceleration of displacement for two sample simulations.</p> "> Figure 5
<p>Relationship between surface displacements and shear displacements for all measurement points.</p> "> Figure 6
<p>Relationship between surface displacements and shear displacements for the three selected locations.</p> "> Figure 7
<p>Shear risk at individual measuring points in three years.</p> "> Figure 8
<p>Trend prediction for total displacement and derivatives: velocity and acceleration for two selected (<b>a</b>,<b>b</b>) benchmarks.</p> ">
Versions Notes

Abstract

:
Monitoring the stability of tailings storage facilities (TSFs) is extremely important due to the catastrophic consequences of instability, which pose a threat to both the environment and human life. For this reason, numerous laboratory and field tests are carried out around dams. An extensive database is collected as part of monitoring and field research. The in-depth analysis of available data can help monitor stability and predict disaster hazards. One of the important factors is displacement, including surface displacements—recorded by benchmarks as well as underground displacements—recorded by inclinometers. In this work, methods were developed to help assess the stability of the TSF in terms of surface and underground displacement based on the simulated data from geodetic benchmarks. The context of spatial correlation was investigated using hot spot analysis, which shows areas of greater risk, indicating the places of correlation of large and small displacements. The analysis of displacements versus time allowed us to indicate the growing exponential trend, thanks to which it is possible to forecast the trend of future displacements, as well as their velocity and acceleration, with the coefficient of determination of the trend matching reaching even 0.97. Additionally, the use of a geographically weighted regression model was proposed to predict the risk of shear relative to surface displacements.

1. Introduction

Tailings storage facilities (TSFs) play a pivotal role in the mining industry, serving as repositories for the bulk of post-flotation tailings generated during ore extraction processes. The escalating global count of TSFs, coupled with emerging instances of failures, underscores the imperative to vigilantly monitor their states. Notably, a solitary failure can yield catastrophic outcomes, inflicting substantial harm to the environment and resulting in loss of life. Refer to Figure 1 for an illustration of countries experiencing the most tailings dam failures between 1915 and 2019 [1].
For these reasons, constant monitoring of dam stability is crucial for early detection and prevention of potential threats. Understanding the sources of failure and implementing prevention methods is essential for ensuring safety. The main causes of TSF failures are slope instability, earthquake loading, overtopping, unsuitable foundations, and seepage [1]. Seismic activity is strongly dependient on the region and in some of them is not relevant, while overtopping can be controlled by proper dam construction and mine production planning. Thus, in this work we focus primarily on slope instability. TSF structures are immensely intricate geotechnical entities, and assuring their stability mandates exhaustive testing, both within the field and in laboratory settings. These tests yield voluminous datasets, encompassing diverse spatial data types, necessitating the formulation of uniform analysis methods. Consequently, this will aid in discerning decision patterns to assist experts. The literature houses a plethora of dam stability analysis methods, which consider a spectrum of security-related concerns and harness data from a range of test types. For instance, in [2], capillary water and its impact on dam stability were examined. The authors demonstrated that capillary phenomena (caused, among other things, by violent rainstorms) have a significant impact on dams, even for several decades after the closure of the TSF. In articles [3,4], authors discussed monitoring systems for dam stability, emphasizing the use of the Internet of Things and cloud computing technologies. Simulation is also an important aspect, as it helps to predict potential scenarios. The authors of article [5] addressed this problem and proposed a simulation method for determining the stability of a closed TSF for solid waste storage. In article [6], the authors proposed an innovative approach to the seepage and stability of tailings dams using numerical simulation. They developed a finite element model based on engineering data from the Lixi tailings dam and presented methodologies for calculating seepage and stability, as well as the total head chart, phreatic line, and safety coefficient of seepage under different working conditions. In turn, ref. [7] demonstrates the efficacy of the finite element method in simulating the consolidation behavior of an upstream tailings dam and reducing the required volume of rockfill berms to ensure dam stability during the phased construction process. Research [8] emphasizes the important problem of instability that can occur in tailing dams made solely from waste rocks. Nonetheless, the study also underscores the efficacy of waste rocks in mining industries. Consequently, that study constitutes a noteworthy stride in comprehending rock-fill tailing dams. Presently, the adoption of machine learning approaches has gained increased traction. Intriguing innovations emerged within the Illumination project, encompassing research conducted at Europe’s largest reservoir, Zelazny Most, which is affiliated with the Polish underground copper ore mines operated by KGHM [9]. For example, in [10], the authors developed a model for tailings classification based on data from SCPT tests. In turn, the paper [11] presents a method for estimating shear wave velocity as well as compression wave velocity. Ref. [12] presents the ML model using anomaly detection techniques for recognizing the transverse shear of layers based on inclinometer measurements.
Surface and underground displacements are considered important parameters to monitor the dam stability. Surface movements are monitored by numerous benchmarks placed on the dam. This is a simple displacement monitoring system from the initial state and has been used for a long time, providing a large amount of historical data for analysis. Underground displacements are monitored using inclinometers, which are instruments placed in the soil that make it possible to monitor horizontal displacements with a probe that passes through a pipe. The gravity sensor in the probe measures the slope to the vertical. Shear zones, which are rapid changes in displacement, can be detected directly from inclinometer measurements, visually from graphs, or automatically by an anomaly detection method. The number of inclinometers in relation to the number of benchmarks on the reservoir is usually much smaller. Therefore, a method was developed to detect the risk of shearing based on the displacements of benchmarks, learned from actual values of displacements resulting from shearing measured by inclinometers. A geographically weighted regression (GWR) model was used to adjust relevant parameters in relation to geographic location.
Despite advancements in TSF monitoring, current methods often lack the ability to detect spatially distributed ground surface displacements with high precision and predictive accuracy. Moreover, traditional monitoring techniques typically require significant on-site instrumentation and are limited in real-time spatial analysis, leaving gaps in early hazard identification and risk prediction for tailings dams. It was also decided to look at the surface displacements themselves, determining their velocity and acceleration. A hot spot analysis method was proposed to detect clusters of high-velocity values or acceleration of displacements, which will provide information on more critical areas of the dam. Another analysis carried out was the determination of the trend of displacement over time. The total value of displacement was found to increase exponentially over time, and fitting the appropriate curve will show how the values will change in the near future. The determination of appropriate derivatives enables the presentation of the trend for the velocity and acceleration of displacements. Displacement analysis is only one of the approaches that can be applied to assess the dam’s stability, and the methods presented should be considered one of the steps in such an assessment.

2. Materials and Methods

2.1. Data Preparation

As mentioned above, the focus was specifically on surface displacements recorded by benchmarks. Simultaneously, this study aimed to investigate the potential relationship between surface displacement and rapid underground displacement, also known as shear zones. To compare these two types of displacement, data standardization was necessary. Shear displacements typically occur in the direction perpendicular to the dam and are measured by inclinometers. This direction of displacement is the most critical. Therefore, this study focused on analyzing the resultant direction of displacement.
The data obtained from benchmark displacement measurements provide information on the displacement in three directions relative to the initial state. The measuring points are placed at different distances from each other around the reservoir, with more benchmarks often placed in critical areas to obtain more precise measurements. Additional measurement points are added to new levels of the dam, resulting in different measurement histories for each point. Measurements are performed at least once a year at each point. The critical value when analyzing the dam stability of the tailings storage facility is the displacement perpendicular to the primary dam, which is indicated by the measurement points around the TSF that show gradual outward displacements. To standardize the data and facilitate analysis of correlation with inclinometer test data, the resultant value of the displacement perpendicular to the primary dam is determined and analyzed consistently. Often, the resultant vector of displacement is directed precisely in this direction or with a slight difference in angle.
In practice, this requires a geometric transformation using vector projection. Basic dam location points have to be used { X i , Y i : i ∈ ( 0 , N ) } . Determining the value of the displacement perpendicular to the dam at each point can be performed according to the following procedure where U x , U y is the displacement in the horizontal directions of the selected benchmark at the location ( x , y ) :
  • Find the closest point ( X k , Y k ) on the basic dam for a given benchmark
    X k , Y k , k ∈ 0 , N : min i ∈ 0 , N   ( X i − x ) 2 + ( Y i − y ) 2
  • Determine the normal vector at this point of the basic dam:
    • Determine the tangent vector to the dam
      X T k = X k + 1 − X k − 1 2 ,   f o r   k ∈ ( 1 , N − 1 ) X k + 1 − X k ,   f o r   k = 0 X k − X k − 1 ,   f o r   k = N ,
      Y T k = Y k + 1 − Y k − 1 2 ,   f o r   k ∈ ( 1 , N − 1 ) Y k + 1 − Y k ,   f o r   k = 0 Y k − Y k − 1 ,   f o r   k = N .
    • Rotate the vector 90 degrees
      X N k = − Y T k Y N k = X T k .
  • Project the displacement vector U → = U x , U y to the normal vector to the dam W → = ( X N k , Y N k ) .
    U N → = U → ° W → | W → | ⋅ W →
  • Calculate of the vector length, i.e., the value of the displacement in the direction perpendicular to the dam.
    U N t = U N →
The displacements calculated in this way in relation to the initial state make it possible to determine the annual increments, which we can treat as the velocity expressed in the units mm/year. And also similarly, accelerations, which will be an increase in velocity. These parameters were used for further analysis.
The most critical displacements are those that result from soil shearing, which can be recorded using inclinometers that measure displacement at various depths from the initial state. The displacement recorded by the inclinometer has a direction perpendicular to the primary dam, which is the same as that obtained after transforming the displacement of benchmarks. The shear zone is defined as the occurrence of rapid and increasing displacement at a specific height over time. The shear zones were identified using a method based on the detection of anomalies using the DBScan algorithm, which is described in detail in [12]. The method uses a clustering algorithm to detect outliers that are not classified into any of the groups. Shears, defined as outliers, are best visible for the value of the derivative of the displacement. A sudden change in the slope of the displacement curve causes a sudden change in its derivative. The displacement value, its derivative, and height are the variables used in the model for shear detection. Based on these variables, the algorithm clusters the data into groups. All values not assigned to any of the groups, i.e., outliers, indicate shearing. To improve the results, the procedure was enhanced by smoothing the raw displacement signal with a median filter to remove noise that should not be considered shearing. However, the final results were validated by removing incorrectly detected shears. For this purpose, the angle of the shear was measured, and those that did not exceed the predetermined value were discarded. The shear zones determined in this way make it possible to determine the size of underground displacements resulting from shear. As in the case of benchmark displacements, it is possible to determine the velocity of these displacements as the value of the annual increment, and similarly acceleration—as the value of the velocity increment.
Benchmarks and inclinometers may be located at various distances from each other, which are often relatively short. There may be a correlation between displacements recorded by devices located close to each other, and it can also be assumed that the displacement at a given point will be influenced by displacements in its vicinity. Therefore, a new variable was introduced to improve the analysis of spatial relationships, which provides information about changes in the neighborhood. This variable is the weighted average of benchmark displacements located within a certain distance from the selected benchmark. The weights were determined using the distance band method, considering the uneven distribution of measuring points. The procedure for calculating the value of the variable is as follows:
  • For each benchmark, a group of n neighbors is determined; these are benchmarks located within a radius smaller than d m a x = 700 m (relative to the Euclidean distance) from the selected benchmark.
  • For each adjacent benchmark, a weight ( w i , i ∈ 1 , n ) is determined inversely proportional to the Euclidean distance ( d i ) (the smaller the distance, the greater the weight, i.e., closer measurements have a greater impact on the result).
    w i ~ 1 d i ,
    where ∑ i = 1 n w i
  • The variable displacement of adjacent benchmarks ( x w ) is calculated as the sum of the products of displacements ( x i ) and weights ( w i ), i.e., the weighted average.
    x w = ∑ i = 1 n w i ⋅ x i

2.2. Methodology

The goal is to establish a series of methods that can be used to evaluate dam stability based on displacements or serve as one of the components in such an evaluation. Three aspects were selected for development: spatial correlation of surface displacements, prediction of shear hazards using surface displacements, and prediction of displacement trends over time. For each of these issues, a solution was devised and tested on actual data.
The hot spots method is a type of local indicator of spatial association (LISA), which was originally proposed by Luc Anselin in 1995 [13]. The aim of LISA is to decompose global spatial statistics into individual observations and identify the locations of correlation clusters. Global spatial statistics, such as Moran’s I, test the null hypothesis of spatial randomness in favor of an alternative hypothesis of clustering across the entire area. In contrast, LISA provides a value for each point in the analyzed space. LISA is defined by two conditions:
  • For each point, return information about the spatial clustering of similar values around that point.
  • The sum is proportional to a statistic of global spatial association [13].
LISA can be written in a general sense as
L i = f y i , y J i
where f is some function, y i is the value of some variable in location i , and y J i are the values in a neighborhood of location i [13].
Therefore, it is necessary to define the neighborhood. There are many methods for this, but the focus is on one distance-based weights matrix. In the analyzed case, this method is appropriate because it is assumed that the closer the measurement is, the greater the impact on the result. In addition, this type of spatial weighting is suitable due to the uneven distribution of measurement points (located at different distances from each other). For example, using the alternative method based on nearest neighbors may result in combining measurement points that are far apart and are not correlated with each other. One of the methods that can be used for LISA is local Moran statistic (a generalization of Moran’s I statistic) which can be defined as
I i = y i − y ¯ 1 n ∑ i y i − y ¯ 2 ∑ j w i j ( y j − y ¯ ) ,
where y i is observation in location i , y ¯ is the mean of y , n is the number of observations, w i j is spatial weights, and j are locations defined as neighboring for i , i.e., j ∈ J i [13].
Like Moran’s I statistic, the hot spots method produces values ranging from −1 to 1, where higher values indicate positive spatial autocorrelation, lower values indicate negative autocorrelation, and values near zero indicate no correlation. However, not all results are statistically significant, so a conditional randomization test can be used to obtain levels of pseudo-significance. This involves randomly permuting the locations of adjacent y j values while keeping the location of y i fixed, and determining the I i statistic for each new dataset to obtain its empirical distribution and statistical significance.
Hot spots, or local spatial clusters, are identified as those groups of locations where LISA is significant. To differentiate between different types of autocorrelation, a Moran scatterplot is used, which plots the values of a variable against the values of its neighbors (Figure 2). On the graph, the solid line is a linear regression, while the dashed lines are mean values. The scatterplot is divided into four rectangles that classify the values according to their spatial associations:
  • Upper right: spatial clustering of similar high values (hot spot).
  • Lower left: spatial clustering of similar low values (cold spot).
  • Upper left: spatial association of dissimilar values, where low values are surrounded by high values (doughnuts).
  • Lower right: spatial association of dissimilar values, where high values are surrounded by low values (diamonds).
Values categorized in this manner can subsequently be represented on a map using suitable color-coding.
Applsci 14 10715 g002
Figure 2. Sample Moran scatterplot.
Figure 2. Sample Moran scatterplot.
Applsci 14 10715 g002
Hot spot analysis can be applied in any scenario where a spatial relationship is desired to identify clusters of high or low values. Crime analysis [14,15,16,17] is one of the most common fields where this method is used. It aims to identify spatial clusters with high crime rates to introduce appropriate solutions for crime prevention. In [16], the authors also analyzed crash data besides crime. The paper [17] compared the hot spot analysis method with Kernel Density Estimation (KDE). Other applications can be found in epidemiology [18,19], economic geography, demographics, traffic incidents, analysis of voting patterns, and retail trade [17]. There are also examples of hot spot analysis applications in geology and geotechnics in the literature. Ref. [20] presents an optimized hot spot analysis method to detect landslides. In turn, ref. [21] presents an analysis of the subsidence problem caused by groundwater withdrawal using Sentinel-1 satellite data and the hot spot method to identify areas of significant subsidence. Sentinel-1 data were also used in [22] to analyze land movement in the Alpine region. The use of hot spot analysis allowed the authors to create a semi-automatic method for extracting moving areas associated with landslides and other mass destruction processes.

2.3. Geografically Weighted Regression

The geographically weighted regression (GWR) method was developed in 1996 [23,24]. The aim of the model is to be able to describe spatial non-stationarity. It makes it possible to identify different dependencies in data at different locations using the multiple regression model. There are numerous examples of GWR model applications in the fields of geology and geotechnics in the literature. One of the most common uses of GWR is for mapping soil organic carbon [25,26,27]. In [25], a model developed using environmental variables such as rainfall, land cover, and terrain type was used to estimate carbon stock. The method was tested on data from Ireland, and the authors described the results as promising. A similar problem was analyzed by the authors of [26] in the case of the Heihe River Basin in China, who compared the performance of GWR and its extended versions (such as geographically weighted ridge regression (GWRR), simple kriging with GWR-derived local means (GWRSK)) with multiple linear regression (MLR). The authors of [27] also applied the extended version of GWRK (i.e., geographically weighted regression kriging) to this problem and found that GWRK increased the precision of the model compared to standard regression kriging. The authors of [28] investigated a similar problem concerning heavy metals in soil, using spatial interpolation, GWR, and self-organizing map methods to identify the relationship between changes in the spatial distribution of heavy metals in soil and human activity. Another topic for the application of GWR is the study of the effect of groundwater on land subsidence [29]. The authors presented results that describe the patterns of spatial influence of aquifers on subsidence zones. Interesting results were also presented for bathymetry data from satellites [30]. The water depth was estimated using an adaptive-geographically weighted regression (A-GWR) model, which gave a determination coefficient above 0.98. The high accuracy of the results and the numerous applications of the GWR model and its modifications demonstrate their usefulness in describing the problem of spatial instability.

2.4. Exponential Trend Prediction

Assuming an exponential trend occurs, the function can be fitted to the data
y t = a   e b t − t 0 + c ,
where y ( t ) is a time series, a and b are fitted constant values, and t 0 is the first value of t .
By analyzing the derivative values of the aforementioned variable (in the discrete case—increase over time), trends can also be identified for these variables:
y ′ t = a b   e b t − t 0 , y ″ t = a b 2   e b t − t 0 .
The exponential curve fitting was performed using the Trust Region Reflective method. To avoid unrealistic estimation values, bounds were set for parameters a, b, and c. The bounds were experimentally determined by performing the curve fitting for all samples initially without constraints. Then, based on the obtained results, intervals were set by taking the highest and lowest values after rejecting outliers using the 1.5 IQR method.

3. Results

All analyses were initially conducted on real data. The dataset was subsequently expanded through a simulation that involved duplicating appropriately distorted values. The distortion was performed by applying a two-dimensional fractional Brownian motion to account for randomness without losing spatial correlation. This method allows for this because it has a long memory property for Hurst parameter greater than 0.5. This is the main reason for choosing this process for simulation. Additionally, the Hurst parameter allows us to adjust the trajectory to the needs of the simulation.
The simulation enabled the assessment of the devised methodologies across diverse scenarios, while faithfully reflecting the character of displacements transpiring at the tailings storage facility dam. The ensuing results, showcased below, have been formulated using simulated data.

3.1. Spatial Autocorrelation of Displacements

In the case of displacements, hot spot analysis was used to study the spatial relationship of velocity and acceleration of displacements in each year. The Moran scatterplot for displacement velocity and acceleration is shown in Figure 3. In the case of velocity, it can be seen that the spatial correlation is greater. This is also shown by the global Moran’s I statistic, which for velocity was on average around 0.4, and for acceleration –0.2.
The visualization of hot spot analysis on the map will display areas with highly correlated values, indicating potential danger zones. This information reveals high velocities or accelerations of displacement at multiple points in a specific area. Mining experts can evaluate the size of this area and the levels of displacements to assess the degree of danger. Conversely, areas classified as cold spots indicate lower probabilities of threat. These areas are characterized by low correlated values of velocity or acceleration of displacements. Additionally, areas with a negative correlation may also be significant. An increase in displacement at one point, without correlation with others, may signify a measurement error or a new phenomenon affecting the neighborhood over time, and thus can be used for anomaly detection. Figure 4 shows some results from the hot spot analysis by location. The black line marks the primary dam. It can be seen that there are both hot spots and cold spots of different sizes. When analyzing the acceleration of benchmark displacement, more statistically insignificant points were observed due to the smaller spatial correlation for this parameter.

3.2. Prediction of Shearing in Relation to Surface Displacements

One of the goals of the study was to develop a model that would be able to indicate the presence of a shear zone in relation to surface displacements. It was assumed that the shear displacements will affect the surface displacement. However, the analysis showed no unequivocal relationship visible at each measurement point. The displacement recorded by benchmarks can be influenced by many factors, and shearing is only one of them. In addition, the nature of the dependence at different dam locations may be different due to the different geological structures and a number of other factors. It was also noticed when comparing the annual increments of benchmark displacements with the increments of displacements caused by shearing in individual locations. There is no correlation in the scattering diagram, and in addition, it can be seen that large surface displacements may appear in places where the amount of shear has not changed (Figure 5). The coefficient of determination R 2 obtained for the relationship between the velocity resulting from shear and the velocity of benchmark displacement for the entire sample is only about 0.03, which indicates a lack of linear relationship between the variables.
When looking at individual locations, it can be seen that there is a certain dependency. The displacement of adjacent benchmarks was also taken into account, for which sometimes there is a greater dependence than in the case of displacements in the same location (Figure 6). For each example, R 2 values were determined for the linear regression fit between both the shear velocity and the displacement velocity of the benchmark at the same location and between the shear velocity and the displacement velocity of adjacent benchmarks. For the presented examples, the values range from 0.27 to 0.84. In some cases, a higher value is obtained for the fit to adjacent benchmarks. This shows that the relationship between underground shear and surface displacement can be partially described by linear regression. However, it is necessary to add a variable related to the location to the analysis. Additionally, it can be seen that not only is the displacement at one specific point valuable information, but also in the adjacent surroundings.
Due to the existence of different relationships in different locations, it was decided to use the GWR model to describe the observed phenomena. It is used to select regression coefficients relative to geographic location. The model uses the independent variables the velocity of benchmark displacement and the velocity of displacement of benchmarks in the vicinity, and the dependent variable is the velocity of displacement resulting from shearing. A model with R 2 = 0.455 and R M S E = 5 was obtained, which means that the accuracy is medium, as it explains about 45% of the values. The second indicator shows the possible expected difference between the predicted and actual value. The obtained value in the case of small shears indicates the possibility of a significant relative difference in values. This confirms the assumption that underground shears do not depend only on surface displacements, but the result can be used to estimate the shear risk. Hence, the decision was made to streamline the presentation of results, focusing solely on the level of risk. Predicted higher shear values correspond to greater risk and lower shear values mean less risk. An exemplary visualization of the results with a comparison of the risk of shearing in three years is shown in Figure 7. Attention should be paid to the changes in risk areas over time. There was an increase first and then a slight decrease, which could imply using measures to reduce displacements. A greater risk is also usually noticeable inside the dam compared to outside.

3.3. Time Displacement Trend Prediction

The ability to predict future phenomena would be of great value for the dam stability analysis. Unfortunately, there are a large number of variable factors that affect the value of displacement increments (velocity and acceleration) in consecutive years, which excludes the possibility of accurate prediction. However, some patterns are repetitive over time. The construction of the next layers of the dam and the pouring out of tailings take place according to a fixed, unchanging system. Therefore, it is possible to search for repeating patterns in displacement values over the years. It was noticed that for the vast majority of cases, there is an increasing exponential trend for the total displacement over time, indicating that displacements are increasing over time. Fitting the trend to the total displacement also makes it possible to indicate the trend for velocity and acceleration, which are the first and second derivatives, respectively. The method developed in this way does not provide accurate information on the value of displacement in subsequent years but is able to indicate its trend, which is equally valuable information.
Figure 8 shows two examples of benchmark displacement measurements with determined trends. It can be seen that the exponential trend describes the behavior of the total displacement well; the value of the R-squared is above 0.9. In the case of velocity and acceleration, the values are already far from the trend, but it is still visible that they are following it. In most cases (including those presented), the velocity has a slight upward trend, and the acceleration is rather constant. However, assuming the occurrence of the trend described by the exponent function, it is known that the acceleration will also start to increase after some time. This moment may be critical for the dam’s stability. The trends have also been projected three years ahead. Although the values are still unknown, the method can identify a trend, allowing for a short-term prediction of the displacement trend over time.

4. Discussion

The results of this study reveal distinct correlations between surface displacement measurements and underlying shear deformations in tailings storage facilities (TSFs), supporting the effectiveness of geodetic monitoring in assessing dam stability. Our findings align with previous studies emphasizing the value of surface displacement as an indicator of subsurface stress dynamics in dam structures, specifically in the context of TSFs where stability is critical for environmental and operational safety. The use of geographically weighted regression (GWR) in this study enhances the spatial resolution of displacement analysis, allowing us to pinpoint areas of potential concern that might otherwise go undetected in standard, location-agnostic models. This location-specific approach not only corroborates existing literature on localized stress effects in TSF structures but also introduces a practical framework for continuous, targeted monitoring that may be more resource-efficient for dam operators.
The broader implications of our findings suggest that by integrating high-resolution displacement monitoring, dam operators can establish proactive maintenance strategies, potentially averting costly or catastrophic failures. While the current study relied on surface measurements, future research should aim to incorporate complementary data such as pore water pressure and geotechnical layer properties to provide a fuller profile of TSF stability. Expanding on these methods to include remote sensing data, such as satellite-based interferometry, could enhance monitoring capabilities further and broaden applicability across various dam types and environments. In addition, exploring the integration of machine learning models with GWR could improve prediction accuracy, presenting a promising direction for enhancing TSF safety protocols. The main obstacle for using the described approach is data availability. Geodetical data are usually collected manually on an annual basis. In cases of dam failures, the dam movement may evolve on a much higher pace, thus continuous displacement data may be necessary. One of the ways to obtain such data is using of GNSS position sensors.
A precise and real-time positioning solution is indispensable for various applications, including geotechnical monitoring of critical areas such as tailings storage facilities (TSFs). Global Navigation Satellite Systems (GNSSs) play a pivotal role in ensuring centimeter/millimeter-level accuracy for these applications.
GNSSs encompass all global positioning technologies relying on satellite constellations, including GPS (USA), GLONASS (Russia), Galileo (Europe), BeiDou (China), IRNSS/NavIC (India), and QZSS (Japan). Each constellation comprises a network of approximately 25 satellites. These satellites operate within the frequency range of 1 GHz to 1.6 GHz, known as the L band. This frequency band is chosen because it exhibits relatively low interference characteristics from the Ionosphere and Troposphere, making it nearly transparent to their effects. Nevertheless, the Ionosphere and Troposphere remain significant sources of potential errors in GNSS accuracy. Signals are transmitted at a power of 44 W using antennas with a gain of 12 dBi. Each GNSS signal comprises three essential components: (1) a carrier signal, (2) an identifier, which serves for both satellite identification and precise timing measurement, and (3) the navigation message. This navigation message contains various critical information, including ephemerides, detailing the satellite’s current position, and almanacs, which provide data about the positions of other satellites in the constellation.
In the mining industry, most GNSS systems make use of concepts such as Differential GNSS (DGNSS) or Real-Time Kinematics (RTK). These systems require reference stations with accurately defined positions, allowing deviations between measured positions and actual positions to be determined. These corrections can then be applied to improve the accuracy of measured positions of other GNSS user receivers [31].
Locating satellites can be a time-consuming process, significantly contributing to overall power consumption. Consequently, there remains a substantial gap in the availability of reliable, fully automated, and cost-effective RTK-GNSS technologies. This gap is especially prominent when considering the rigorous energy efficiency demands of low-power IoT devices intended for distribution along TSFs. When designing an IoT GNSS node for TSF monitoring, optimizing all operational parameters becomes imperative. This optimization must consider the unique challenges posed by potential multipath interference or satellite blockage within mine infrastructures.
The primary parameters to be considered for an IoT GNSS solution include the following:
  • A power consumption goal, to ensure a lifespan of multiple years without the need for battery replacement.
  • Available bandwidth of communication channels, such as LoRa coverage.
  • Line of sight to the sky and any limitations imposed by the specific configuration of the TSF.
Taking these parameters into account is crucial for the development of an efficient and effective IoT GNSS solution specifically tailored to meet the demands of TSF monitoring. Given this context and the potential added value of obtaining absolute position readings over time, as well as the advantages of enhancing techniques for measuring TSF displacement data, continuous efforts are being made to develop commercial technologies that can fulfill these requirements [32].

5. Conclusions

Tailings storage facilities are essential objects in the mining industry that have to be attentively monitored. Their stability is crucial and can be disturbed by many factors. Hence, it is important to establish an accurate model that can make it possible to prevent catastrophes. The analysis described in this article focuses on the displacements recorded by benchmarks and correlates them with shear zones determined from inclinometer measurements. The location and spatial dependencies are key, so the hot spot and geographically weighted regression methods were taken into consideration. The first one, based on global spatial statistics, categorizes data into four groups: spatial clustering of similar high values (hot spot), spatial clustering of similar low values (cold spot), and two groups with dissimilar values. One of possible causes of displacement is shearing, thus the data from benchmarks were correlated with the data from inclinometers. The authors showed that in some individual locations, it is possible to observe such a dependency. Hence, the geographically weighted regression model was used to describe the problem. Due to its insufficient accuracy, the results were simplified to present only the level of risk. It was emphasized that the changes in risk areas over time are important to monitor. In the end, trend prediction for total displacement and derivatives for benchmarks is discussed. This approach can be useful for decision-making about the construction of the next layers of the dam. Particularly, in case of identification of high spatial correlation any further construction of the dam should be preceded with dam reinforcement in those regions.

Author Contributions

Funding acquisition, P.S. and F.H.-R.; Methodology, W.K. and S.A.; Project administration, S.A., F.H.-R. and I.K.; Software, W.K. and M.S.; Supervision, P.S.; Visualization, W.K. and M.S.; Writing—original draft, W.K. and P.S.; Writing—review and editing, M.S., S.A., F.H.-R. and I.K. All authors have read and agreed to the published version of the manuscript.

Funding

This work has received funding from EIT RawMaterials GmbH under Framework Partnership Agreement No. 21123 (project Sec4TD).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

Authors W.K., P.S., M.S. and S.A. were employed by the company KGHM Cuprum (Poland). Authors F.H.-R. and I.K. were employed by the company Worldsensing (Spain). The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

References

  1. Clarkson, L.; Williams, D. Critical review of tailings dam monitoring best practice. Int. J. Min. Reclam. Environ. 2020, 34, 119–148. [Google Scholar] [CrossRef]
  2. Zandarín, M.T.; Oldecop, L.A.; Rodríguez, R.; Zabala, F. The role of capillary water in the stability of tailing dams. Eng. Geol. 2009, 105, 108–118. [Google Scholar] [CrossRef]
  3. Sun, E.; Zhang, X.; Li, Z. The internet of things (IOT) and cloud computing (CC) based tailings dam monitoring and pre-alarm system in mines. Saf. Sci. 2021, 50, 811–815. [Google Scholar] [CrossRef]
  4. Dong, L.; Shu, W.; Sun, D.; Li, X.; Zhang, L. Pre-alarm system based on real-time monitoring and numerical simulation using internet of things and cloud computing for tailings dam in mines. IEEE Access 2017, 5, 21080–21089. [Google Scholar] [CrossRef]
  5. Coulibaly, Y.; Belem, T.; Cheng, L. Numerical analysis and geophysical monitoring for stability assessment of the Northwest tailings dam at Westwood Mine. Int. J. Min. Sci. Technol. 2017, 27, 701–710. [Google Scholar] [CrossRef]
  6. Zhang, C.; Chai, J.; Cao, J.; Xu, Z.; Qin, Y.; Lv, Z. Numerical simulation of seepage and stability of tailings dams: A case study in Lixi, China. Water 2020, 12, 742. [Google Scholar] [CrossRef]
  7. Leong, W.K.; Chu, J. Effect of undrained creep on instability behaviour of loose sand. Can. Geotech. J. 2002, 39, 1399–1405. [Google Scholar] [CrossRef]
  8. Sitharam, T.G.; Hegde, A. Stability analysis of rock-fill tailing dam: An Indian case study. Int. J. Geotech. Eng. 2017, 11, 332–342. [Google Scholar] [CrossRef]
  9. Llumineation. Available online: https://www.illumineation-h2020.eu (accessed on 23 September 2024).
  10. Koperska, W.; Stachowiak, M.; Duda-Mróz, N.; Stefaniak, P.; Jachnik, B.; Bursa, B.; Stefanek, P. The Tailings Storage Facility (TSF) stability monitoring system using advanced big data analytics on the example of the Żelazny Most Facility. Arch. Civ. Eng. 2022, 68, 297–311. [Google Scholar]
  11. Duda, N.; Jachnik, B.; Stefaniak, P.; Bursa, B.; Stefanek, P. Tailings storage facility stability monitoring using CPT data analytics on the Zelazny Most facility. In Proceedings of the Application of Computers and Operations Research in the Mineral Industries (APCOM 2021): Minerals Industry 4.0: The Next Digital Transformation in Mining, Johannesburg, South Africa, 30 August 2021; ISBN 978-1-928410-26-3. [Google Scholar]
  12. Koperska, W.; Stachowiak, M.; Jachnik, B.; Stefaniak, P.; Bursa, B.; Stefanek, P. Machine Learning Methods in the Inclinometers Readings Anomaly Detection Issue on the Example of Tailings Storage Facility. In IFIP International Workshop on Artificial Intelligence for Knowledge Management; Springer: Cham, Switzerland, 2021; pp. 235–249. [Google Scholar]
  13. Anselin, L. Local indicators of spatial association—LISA. Geogr. Anal. 1995, 27, 93–115. [Google Scholar] [CrossRef]
  14. Chakravorty, S. Identifying crime clusters: The spatial principles. Middle States Geogr. 1995, 28, 53–58. [Google Scholar]
  15. Ratcliffe, J. Crime mapping: Spatial and temporal challenges. In Handbook of Quantitative Criminology; Springer: New York, NY, USA, 2010; pp. 5–24. [Google Scholar]
  16. Kuo, P.F.; Lord, D.; Walden, T.D. Using geographical information systems to organize police patrol routes effectively by grouping hotspots of crash and crime data. J. Transp. Geogr. 2013, 30, 138–148. [Google Scholar] [CrossRef]
  17. Kalinic, M.; Krisp, J.M. Kernel density estimation (KDE) vs. hot-spot analysis–detecting criminal hot spots in the City of San Francisco. In Proceedings of the 21st Conference on Geo-Information Science, Lund, Sweden, 12–15 June 2018. [Google Scholar]
  18. Kirby, R.S.; Delmelle, E.; Eberth, J.M. Advances in spatial epidemiology and geographic information systems. Ann. Epidemiol. 2017, 27, 1–9. [Google Scholar] [CrossRef] [PubMed]
  19. Shaweno, D.; Karmakar, M.; Alene, K.A.; Ragonnet, R.; Clements, A.C.; Trauer, J.M.; Denholm, J.T.; McBryde, E.S. Methods used in the spatial analysis of tuberculosis epidemiology: A systematic review. BMC Med. 2018, 16, 193. [Google Scholar] [CrossRef] [PubMed]
  20. Lu, P.; Bai, S.; Tofani, V.; Casagli, N. Landslides detection through optimized hot spot analysis on persistent scatterers and distributed scatterers. ISPRS J. Photogramm. Remote Sens. 2019, 156, 147–159. [Google Scholar] [CrossRef]
  21. Khan, S.D.; Gadea, O.C.; Tello Alvarado, A.; Tirmizi, O.A. Surface Deformation Analysis of the Houston Area Using Time Series Interferometry and Emerging Hot Spot Analysis. Remote Sens. 2022, 14, 3831. [Google Scholar] [CrossRef]
  22. Solari, L.; Del Soldato, M.; Montalti, R.; Bianchini, S.; Raspini, F.; Thuegaz, P.; Bertolo, D.; Tofani, V.; Casagli, N. A Sentinel-1 based hot-spot analysis: Landslide mapping in north-western Italy. Int. J. Remote Sens. 2019, 40, 7898–7921. [Google Scholar] [CrossRef]
  23. Brunsdon, C.; Fotheringham, A.S.; Charlton, M.E. Geographically weighted regression: A method for exploring spatial nonstationarity. Geogr. Anal. 1996, 28, 281–298. [Google Scholar] [CrossRef]
  24. Wheeler, D.C.; Páez, A. Geographically weighted regression. In Handbook of Applied Spatial Analysis; Springer: Berlin/Heidelberg, Germany, 2010; pp. 461–486. [Google Scholar]
  25. Zhang, C.; Tang, Y.; Xu, X.; Kiely, G. Towards spatial geochemical modelling: Use of geographically weighted regression for mapping soil organic carbon contents in Ireland. Appl. Geochem. 2011, 26, 1239–1248. [Google Scholar] [CrossRef]
  26. Song, X.D.; Brus, D.J.; Liu, F.; Li, D.C.; Zhao, Y.G.; Yang, J.L.; Zhang, G.L. Mapping soil organic carbon content by geographically weighted regression: A case study in the Heihe River Basin, China. Geoderma 2016, 261, 11–22. [Google Scholar] [CrossRef]
  27. Kumar, S.; Lal, R.; Liu, D. A geographically weighted regression kriging approach for mapping soil organic carbon stock. Geoderma 2012, 189, 627–634. [Google Scholar] [CrossRef]
  28. Wang, Z.; Xiao, J.; Wang, L.; Liang, T.; Guo, Q.; Guan, Y.; Rinklebe, J. Elucidating the differentiation of soil heavy metals under different land uses with geographically weighted regression and self-organizing map. Environ. Pollut. 2020, 260, 114065. [Google Scholar] [CrossRef] [PubMed]
  29. Yu, H.; Gong, H.; Chen, B.; Liu, K.; Gao, M. Analysis of the influence of groundwater on land subsidence in Beijing based on the geographical weighted regression (GWR) model. Sci. Total Environ. 2020, 738, 139405. [Google Scholar] [CrossRef] [PubMed]
  30. Vinayaraj, P.; Raghavan, V.; Masumoto, S. Satellite-derived bathymetry using adaptive geographically weighted regression model. Mar. Geod. 2016, 39, 458–478. [Google Scholar] [CrossRef]
  31. Li, X.; Ge, M.; Guo, B.; Wickert, J.; Schuh, H. Temporal point positioning approach for real-time GNSS seismology using a single receiver. Geophys. Res. Lett. 2013, 40, 5677–5682. [Google Scholar] [CrossRef]
  32. Securing Tailings Dam Infrastructure with an Innovative Monitoring System. Available online: https://sec4td.fbk.eu/ (accessed on 23 September 2024).
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Figure 1. Countries with the highest number of TSF dam failures (in the period 1915–2019).
Figure 1. Countries with the highest number of TSF dam failures (in the period 1915–2019).
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Figure 3. Moran scatterplot for displacement velocity (a) and displacement acceleration (b).
Figure 3. Moran scatterplot for displacement velocity (a) and displacement acceleration (b).
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Figure 4. Hot spot analysis result for velocity and acceleration of displacement for two sample simulations.
Figure 4. Hot spot analysis result for velocity and acceleration of displacement for two sample simulations.
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Figure 5. Relationship between surface displacements and shear displacements for all measurement points.
Figure 5. Relationship between surface displacements and shear displacements for all measurement points.
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Figure 6. Relationship between surface displacements and shear displacements for the three selected locations.
Figure 6. Relationship between surface displacements and shear displacements for the three selected locations.
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Figure 7. Shear risk at individual measuring points in three years.
Figure 7. Shear risk at individual measuring points in three years.
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Figure 8. Trend prediction for total displacement and derivatives: velocity and acceleration for two selected (a,b) benchmarks.
Figure 8. Trend prediction for total displacement and derivatives: velocity and acceleration for two selected (a,b) benchmarks.
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MDPI and ACS Style

Koperska, W.; Stefaniak, P.; Stachowiak, M.; Anufriiev, S.; Kakogiannos, I.; Hernández-Ramírez, F. Spatial and Temporal Analysis of Surface Displacements for Tailings Storage Facility Stability Assessment. Appl. Sci. 2024, 14, 10715. https://doi.org/10.3390/app142210715

AMA Style

Koperska W, Stefaniak P, Stachowiak M, Anufriiev S, Kakogiannos I, Hernández-Ramírez F. Spatial and Temporal Analysis of Surface Displacements for Tailings Storage Facility Stability Assessment. Applied Sciences. 2024; 14(22):10715. https://doi.org/10.3390/app142210715

Chicago/Turabian Style

Koperska, Wioletta, Paweł Stefaniak, Maria Stachowiak, Sergii Anufriiev, Ioannis Kakogiannos, and Francisco Hernández-Ramírez. 2024. "Spatial and Temporal Analysis of Surface Displacements for Tailings Storage Facility Stability Assessment" Applied Sciences 14, no. 22: 10715. https://doi.org/10.3390/app142210715

APA Style

Koperska, W., Stefaniak, P., Stachowiak, M., Anufriiev, S., Kakogiannos, I., & Hernández-Ramírez, F. (2024). Spatial and Temporal Analysis of Surface Displacements for Tailings Storage Facility Stability Assessment. Applied Sciences, 14(22), 10715. https://doi.org/10.3390/app142210715

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