Quantitative assessments in landslide susceptibility evaluation are typically dominated by statistical analyses. However, this paper employs a deterministic approach to construct such maps, specifically focusing on the stability assessment of shallow landslides with slip surfaces generally not exceeding 5 m in depth at a regional scale. The study area chosen for this research is the landslide-prone region between Hlohovec and Sereď towns in the central-western part of Slovakia. Our focus is on the activation of shallow landslides, representing the youngest, third generation of landslide evolution in the area. For the stability assessment, three scenarios were considered using deterministic analysis: a scenario involving dry slopes, a scenario under partially saturated conditions, and a scenario of fully saturated slopes. This approach enables the assessment of stability conditions based on qualitative parameters derived from both field and laboratory research. The results from the deterministic analysis aid in defining different stages of activity within the landslide body. These Landslide susceptibility maps were verified directly in the field, and most landslides reactivated from 2011 to the present fell into the class with the safety factor below 1.0. In comparison with the landslide hazard map created by using bivariate statistical analysis, it was observed that 89.97% of the area is in a very high level of landslide hazard, given a safety factor below 1.0. This highlights the effectiveness of the deterministic approach in capturing the vulnerability of the region to shallow landslides.
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Introduction
The global trend of technosphere development, particularly in areas with adverse geological and geomorphological conditions, has escalated with the increasing population, a phenomenon that is also evident in Slovakia. The assessment of landslide hazards holds significant importance in our country due to its geological structure, especially in zones such as Carpathian flysch, Paleogene, Mesozoic of Klippen belt, and the borders of Neovolcanites. These geological conditions are conducive to the activation of slope deformations. By 2008, slope deformations had covered approximately 5.25% of Slovakia’s total area, a percentage that has likely increased following extreme precipitation in 2010 and subsequent floods in the eastern part of the country. Knowing that slope deformations are the most widespread and most dangerous geohazard occurring here, it is imperative to place strong emphasis on selecting appropriate construction areas and assessing site stability.
The application of Geographic Information Systems (GIS) has become integral in landslide hazard assessment, with most analyses relying on quantitative methods, particularly statistical ones (Ercanoglu et al. 2004; Lee and Pradhan 2007; Yilmaz and Keskin 2009; Gokceoglu and Sezer 2009; Yilmaz 2009a, b, 2010a, b; Pradhan and Lee 2010; Pourghasemi, 2012; Bednarik et al. 2012; Holec et al. 2013; Erener et al. 2016; Zhao et al. 2019; Stefanelli et al. 2020). GIS offers robust functions not only in database processing but also in geostatistical analysis, facilitating the creation of hazard maps through various methods. Generally, the methods of landslide hazard assessment are divided into two groups – qualitative and quantitative (in terms of classification according to Aleotti and Chowdhury 1999).
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Quantitative methods, predominantly statistical ones, have been the primary choice for landslide hazard assessment due to their effectiveness. The way of interpreting the final hazard classes is one of the basic differences between the deterministic and statistical methods (besides the methodology of the assessment). The final classes of landslide hazard maps created by statistical methods, represent the susceptibility of the area to the landslide activation. Deterministic analysis directly define the stability conditions, allowing for the comparison of multiple stability scenarios.
Quantitative statistical methods are particularly effective for regional landslide hazard assessments in a GIS environment. However, assessing the slope stability of larger areas poses challenges in terms of time and economic feasibility, as detailed input data are essential. This limitation makes such assessments more suitable for specific site areas using physically based or deterministic approaches. The lack of detailed input data, especially geotechnical soil properties, is a notable disadvantage, further compounded by technical and financial constraints associated with engineering geological surveys.
The selected landslide area between the Hlohovec and Sereď towns represents an ideal “laboratory” for the study of landslide hazard in a GIS environment. It features not only a sufficient density of existing slope deformations, making it suitable for statistical processing of landslide hazard, but also serve a wide range of detailed engineering geological research and monitoring which has been carried out over the last 30 years. These surveys provide an extensive dataset, including geological, geotechnical, and hydrogeological information, essential for deterministic analyses.
Deterministic approaches in landslide hazard assessment
Landslide hazard assessment by deterministic analyses requires a relatively high precision and variability of input parameters. For that reason, the application of this method has been limited to small areas on a large map scale with homogeneous geomorphologic and geological conditions in most cases. However, its application at small to medium scales is hindered by the lack of detailed input data, particularly geological, geotechnical, and hydrogeological information, which must be determined in the field or laboratory.
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Despite these challenges, deterministic methods have been successfully applied at a regional scale using GIS by van Westen (1993); Terlien et al. (1995); van Westen and Terlien (1996). Researches carried out by Pack et al. (1998, 2001) and Zaitchik et al. (2003) were among the first studies of regional stability assessment by deterministic analyses in GIS, which created a complex model combining the slope stability model and the steady-state hydrology model. Prediction of shallow landslides and regional modelling using a combination of the transient rainfall infiltration model and the slope stability analyses were explored by Baum et al. (2005) and Salciarini et al. (2006). A noteworthy comparative study on statistical and deterministic methods for shallow landslide susceptibility mapping in clayey soils was conducted by Ciurleo et al. (2017), providing insightful results.
While deterministic methods in GIS allow the simulation of multiple scenarios based on variable trigger factors, comprehensive studies within this field remain relatively rare. The processing of landslide hazard assessment using deterministic methods involves employing various models, ranging from simple infinite slope models to complex 3D models. These deterministic models operate based on physical laws, conserving mass, energy, or momentum (Terlien 1996).
The use of GIS in deterministic method allows the simulation of multiple scenarios, based on the hypothesis of the variability trigger factors and compilation of relatively reliable landslide hazard maps (Jelínek 2005). The separately infinite slope stability model (Fig. 1) is the only model that calculates the stability of each unit cell of the slope in GIS environment. However, its application requires careful considerations and simplifications, as outlined by Jelínek (2007). These include the necessity for detailed geotechnical, hydrogeological, and morphological input data, limiting its use to small areas on a large map scale. Additionally, it is tailored for assessing shallow landslides, assuming planar shear plane areas parallel to the surface and the merging of soil layers into a single layer. The quasi-homogeneous geological and geomorphologic conditions must be met, and a correct justification of potential failure mechanisms and causes for landsliding is essential.
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Landslide hazard assessment within a selected area using the deterministic method is quantified through the factor of safety (FS), calculated for all slopes within the region. The final classification of landslide hazard is derived by dividing the calculated factor of safety. The degree of factor of safety is determined as the ratio of all passive forces (resisting forces against sliding) to all active forces (driving forces). If the resulting factor of safety is less than 1.0, it indicates a potential for movement.
Interval from 1.0 to 1.5 is divided here according to the requirements of civil engineers and building designers. From the point of view of slope stability, a value below 1 represents an unstable slope, equal to 1 is equilibrium and a value above 1 represents a stable slope. For temporary buildings, statics require a value of 1.25 and for permanent buildings above 1.5. So, only from this point of view we define these slopes as potentially unstable. Otherwise, from the point of view of the engineering geologist, these slopes are stable, but to the builder provide information that he must design some support structure to increase the degree of stability for the permanent construction.
Acceptable limits for factor of safety values vary depending on the intended land use. For instance, recommended values range from 1.0 to 1.5 for different land-use purposes, such as 1.5 in urban zones, 1.1 in agricultural lands, woodlands, fields, and meadows, and 1.0 in certain other land-use scenarios. For the intravillans of towns and villages from the point of view of building statics and geotechnical approach, the requirements for the factor of safety for temporary buildings are 1.3 and for permanent buildings 1.5.
The factor of safety is calculated using various formulas, and in the deterministic method, Eq. 1 is applied, following the suggestion by Bruden and Prior (1979, cited in van Westen 1993). The formula for factor of safety (FS) calculation is as follows:
hw/z – the ratio of the height of groundwater table level above the slip surface hw [m] and the slip surface depth z [m]
The deterministic method is specifically designed for landslide assessments involving shallow slip surfaces, such as shallow landslides or those where the ratio of slip surface depth to the length of the landslide is less than 0.1 (Terlien 1996). In the analysis, the parameter “m” plays a crucial role in representing different hydrogeological conditions up to a depth of 5.0 m across the entire area. A value of 0.0 for “m” signifies dry conditions, indicating that groundwater has no influence on slope stability. In such cases, the slope angle becomes the primary factor influencing overall stability. A value of 0.5 for “m” indicates wet, partly saturated conditions of the slope. When “m” is set to 1.0, the slopes up to a depth of 5 m are considered saturated.
Within the modelled area of Hlohovec – Sereď (Fig. 2), three generations of landslides have been identified. Recent observations indicate the activation of the youngest, third generation, characterized by shallow slip surfaces not exceeding 5 m in depth. It is important to note that the depth of the failure slip surface has been uniformly chosen as 5 m for the entire landslide area, considering the prevalence of shallow landslides.
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According to the wide range of engineering geological research and investigations carried out in this area during previous years there are a lot of available data, which allow an accurate process of the deterministic landslide hazard in the selected larger area in GIS. Geotechnical parameters (cef, φef and γ) were obtained from mentioned studies. Within the study area more than 270 engineering geological boreholes (Fig. 3) were drilled, and more than 440 undisturbed and 580 disturbed soil samples were taken. These boreholes were concentrated mainly to the left side of the modelled area. Boreholes were situated at the landslides evolved on the western part of Nitrianska pahorkatina Upland, on the contact of Upland and alluvial plain of the Váh River.
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The processing of input data, for example, the spatial variability of data, sampling error or material properties could induce some limitations of the chosen method. According to the density of the geotechnical data in the wider area, interpolation methods must be applied. A wide range of interpolation methods is used in the GIS environment. In GIS environment, a wide range of interpolation methods are generally implemented. In this study, the interpolation methods utilized include IDW (inverse distance weighting), Spline, and Kriging. There are different specifications which could cause an inaccuracy to the final map, and therefore, the correct method must be selected. The difference in the spatial distribution of the interpolated final maps of the input parameters is the reason why three interpolation methods were used. Taking into account that all available pointed geotechnical data were used in the process of interpolation, it was not possible to validate the result of the geotechnical maps. Therefore, the partial landslide hazard maps were created for different scenarios. The final hazard maps for each modelled scenario were then derived by overlaying these partial landslide hazard maps. The entire process of landslide hazard assessment using the deterministic method is visually represented in the flowchart provided in Fig. 4.
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Characteristics of the landslide area
The western boundary of the Nitrianska pahorkatina Upland, specifically the section between the towns Hlohovec and Sereď, meets all the specified criteria. Since the late 1950s, plans have been in motion for the construction of a water reservoir with a power plant in this area. The proposed Hlohovec – Sereď water project is envisioned to be a vital component of the Váh River waterway, slated for use as an international water route. Additionally, the region is marked by significant industrial and agricultural development.
The study area encompasses 44.3 km², with a total affected area reaching 5.97 km², equivalent to 13.5% of the study area. The Váh River represents the natural boundary (barrier) on the left side. From the right side, from the north to the south, the boundary line passes along the lowest contours between the two slopes or passes directly beneath the slope.
The slopes on the left side of the Váh River exhibit a high frequency of slope deformations, posing potential risks to the planned water work construction. According to the classification of slope movements, within the study area various types of slope movements occur, with creeping and sliding being predominant. Landslides are characterized by retrogressive evolution. Otepka et al. (1983) divided all landslides occurring between Hlohovec and Sereď into three generation groups based on morphology of slopes, form, and activity. Among these, the third generation is the youngest, characterized by shallow slip surfaces, and represents the initial stage of landslide evolution in the area.
Geologically, the region comprises Neogene rocks (Pliocene) covered by Quaternary sediments of varying thickness. Quaternary sediments are formed by fluvial deposit of the Váh River, eolian-slope and proluvial deposits. Sediments of upper Neogene/Pliocene are in the Nitrianska pahorkatina Upland at depths from 0.3 to 0.7 m below the terrain, in the depths of 8.0–20.0 m in the alluvial plane. Neogene sediments forms a massive complex of clays and sands with occasional lenses of sandstones and conglomerates. The geological structure of sliding slopes features alternating layers of high plastic impermeable clays and fine-grained sand aquifers with artesian water, providing a conducive environment for the development of slope failures.
Input parameters
In addition to soil properties (geotechnical parameters) and hydrological conditions, having data related to geomorphology, particularly the slope angle, is crucial in landslide hazard assessment. The depth of the shear slip surface is also an essential parameter for a comprehensive analysis. The slope angle is particularly significant as it represents one of the most important geomorphological factors in the stability analysis within the deterministic method.
Slope angle
The relative elevation of slopes over the alluvial plain varies within the assessed area. In the northern part around Hlohovec town, the elevation changes between 120 and 150 m. In contrast, in the southern part near Šintava village, the change is only between 15 and 20 m. The digital elevation model (DEM) of the selected area is depicted in Fig. 5a.
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The slope angle (rate of gradient altitudes) mainly determines the flow velocity of materials down to the slope and in combination with other parameters significantly affects the stability conditions. Each slope has a critical angle value, beyond which stability conditions change, leading to potential sliding. This value is influenced by the properties of rock material affecting both the active forces (along the sliding) and passive forces (counter sliding) operating in the slope. The crossable value of slope angle depends on the basic strength characteristics of soil forming the slope – internal friction angle (φ) and cohesion (c).
In general, non-cohesive soils without the impact of groundwater must maintain slope stability when the slope angle (α) is smaller, at most equal to the angle of internal friction (φ) of the soil forming the slope. This angle can be quite large, reaching up to 35 °.
Slope angle (Fig. 5b) was calculated from the DEM with a 1° interval, and the value representing the slope angle (size 5 × 5) was determined as the maximum rate of slope angle and distance between the given cell and its eight neighbouring cells, i.e. the steepest slope was defined.
Geotechnical input parametric maps
Geotechnical properties of soils within a depth of 5 m under the terrain were analyzed, with a total of 178 soil samples processed in the laboratory. The interpolation process (Table 1) considered averages when multiple samples were taken from one well. Out of the 178 samples, 85 points were selected for final processing, as illustrated in Fig. 3b.
Table 1
Example of averages of selected physical properties of soil samples from the borehole HSV-80.
Points
depth of sampling
h [m]
liquid limit
wl [%]
plastic limit
wp [%]
plasticity index
Ip [%]
consistency index
Ic
lithology
HSV-80
1.10–1.30
45.80
19.40
26.40
0.97
silt with high plasticity
2.10–2.30
54.40
20.70
33.70
0.76
clayey loam
3.80–4.00
64.40
20.20
44.20
0.57
clayey loam
Average
54.87
20.10
34.77
0.77
The soils samples were classified according to the STN EN 73 1001 (2011) based on borehole logs and laboratory tests of Atterberg limits, consistency index and degree of saturation. The basic statistical characteristics of the selected qualitative parameters of soil samples are presented in Table 2.
Table 2
Basic statistical characteristics of selected qualitative parameters of the evaluated soil samples
Basic statistical characteristics
liquid limit
Wl [%]
plastic limit
Wp [%]
plasticity index
Ip [%]
consistency index
Ic
degree of saturation
Sr [%]
average
51.91
19.55
32.29
1.04
79.66
median
51.00
19.40
31.90
1.03
83.60
maximum
85.30
27.80
60.10
1.77
100.00
minimum
26.00
13.40
5.40
0.49
16.20
standard deviation
13.95
3.07
12.53
0.18
17.23
The stability calculations (using Formula 1.0) utilized the interpolated standard characteristics of geotechnical parameters specified in STN EN 73 1001 (2011). The spatial distribution maps of these input parameters are displayed in Fig. 6. Each parameter map was classified into five intervals for mutual comparison. The output maps were characterized by significant differences in class zoning. Maps of soil unit weight, maps of effective cohesion c [kPa] and effective friction angle φef [°] were divided into the following 5 intervals:
The spatial distribution of classes and the frequency of landslides within each class are summarized in Tables 3 and 4. The input parametric maps used in the analysis were not reclassified into classes in order to preserve the detailed information contained in cells with a size of 5 × 5 m. To mitigate the strong influence of low slope angles (ranging from 0° to 1°), the “ceil” function was employed to round up the integral numbers. In this case, the minimal value of the slope angle in the area was set to 1.
Table 3
Basic statistical characteristics of shear parameters and unit weight of soil of interpolation points
Basic statistical characteristics
φef [°]
cef [kPa]
γ [kN.m-3]
average
16.71
8.49
20.17
median
15.00
8.00
20.50
maximum
28.00
20.00
21.00
minimum
13.00
0.00
18.00
standard deviation
3.95
4.98
0.92
Table 4
Basic statistical comparison of interpolating values of each input parametric maps compiled by IDW, Spline and Kriging method
Method of interpolation
IDW
Spline
Kriging
input map
min
max
average
min
max
average
min
max
average
Map of the unit weight of soil
18.00
21.00
20.27
16.37
22.30
20.12
18.60
21.00
20.17
Map of cohesion
0.00
19.99
8.38
0.75
22.90
9.12
3.20
17.30
8.69
Map of friction angle
13.00
27.99
16.73
6.66
28.98
17.48
13.00
22.30
17.19
Stability assessment in landslide hazard analysis
The stability assessment of the study area was conducted by creating parametric input geotechnical maps through GIS interpolation methods. Three distinct landslide hazard maps were developed to represent different stability scenarios corresponding to various saturation states of the slope under different climatic conditions.
The precision and reliability of the final hazard map depend on both a comprehensive understanding of the area and the quality of the input data, particularly the geotechnical maps. The acquisition and creation of these input maps are critical components of landslide hazard assessment. Given that each interpolation method introduces some degree of error into the analysis, the final map for each model scenario was generated by overlaying the resulting maps with three input maps compiled using the same interpolation method. Final hazard maps were reclassified into four classes based on the results of the degree of safety factor: < 1.0; 1.0 to 1.25; 1.25 to 1.5 and > 1.5. Areas where the degre of FS is less than 1.0 are considered as the areas with unstable conditions. Areas with intervals of FS < 1.0 to 1.25 > and < 1.25 to 1.5 > are considered as potential unstable for temporary constructions, or for permanent buildings and the areas with the final degree of FS greater than 1.5 are considered stable.
The calculated values of FS were primarily used for comparing each stability scenario. Additionally, these values help identify unstable parts of the modeled area. The zones with the lowest stability, where the degree of the factor of safety was calculated to be less than 1.0, were identified, even at scenarios representing dry slope conditions without the influence of groundwater.
Scenario of dry slope
The scenario of a dry slope represents the simplest modeled condition without the influence of groundwater. In this scenario, the assumption is made that the input parameter “m,” defined as the ratio of the depth of the shear surface to the groundwater table levels, is equal to zero. This implies the absence of groundwater within the slope, leading to the removal of the unit weight of water parameter from Eq. 1. In the GIS environment, the following formulas (Eqs. 2, 3, 4) were employed to create partial hazard maps for this specific scenario:
idw_c; Spline_c; Kriging_c - parametric map of effective cohesion compiled by IDW, Spline and Kriging method;
idw_gama; Spline_gama; Kriging_gama - parametric map of the unit weight of soils compiled by IDW, Spline and Kriging method;
idw_fi; Spline_fi; Kriging_fi - parametric map of effective internal friction angle of soils compiled by IDW, Spline and Kriging method;
slope - parametric map of slope angle.
The final landslide hazard map for the scenario of a dry slope represents a comprehensive assessment of slope stability in the analyzed area. The map is a result of overlaying three reclassified partial hazard maps, each corresponding to a specific stability scenario based on different climatic conditions. On the left map (Fig. 7.a), visible the raster cells (size 5 × 5) contained the same information – the same value of factor of safety has been calculated for each cell. That is, there was a pairing of unstable, potentially stable and stable state regions, which was specifically calculated for each map with different input geotechnical maps. The white shade indicates the cells in which another security factor was calculated - mismatched fields. Hereafter signed in the text as map A. The creation of Map B (Fig. 7b) in the dry slope scenario involved marking all-unstable areas, which are cells where the factor of safety (FS) was calculated to be less than 1.0 in at least one of the partial landslide hazard maps. In other words, Map B represents areas that were consistently identified as unstable in the overlay of partial hazard maps, even if there were discrepancies in FS values among the different scenarios.
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Figure 8a and b show the spatial distribution of the landslide hazard classes including the size of class with which the cells do not match. The size of the unstable area, FS was less than 1.0 in each partial map, is relatively small (0.34 km2; 0.77% of the total assessed area). If we consider the entire area with unstable conditions calculated in all partial maps (not only matched), the size of the unstable area almost doubled to 0.64 km2 (1.4%). Unstable conditions are mainly on the contact of the slopes of Nitrianska pahorkatina Upland and alluvial plain of the Váh River.
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Conditionally stable areas (class 2 and 3) reach an area 0.48 km2 (1.08%) of the total area. Stable areas have a spatial distribution more than 95% of the total area. In both cases, the calculated FS is almost equal, follows the difference between the partial hazard maps.
Scenarios of partially and fully saturated slope
In natural conditions, the model situation of a dry slope hardly occurs. Groundwater occurs at various depths on slopes where vertical uplift due to hydrostatic pressure affects stability conditions. The spatial distribution of the landslide hazard classes of the final maps and the percentage distribution of the landslide hazard classes of the final maps for the partially saturated and fully saturated slope scenario can be seen in Figs. 9, 10, 11 and 12.
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Verification process
The accuracy of landslide susceptibility maps was rigorously assessed through on-site field verification. Particularly, reactivated landslides occurring between 2010 and 2011 were extensively examined, with a specific focus on those displaying a factor of safety below 1.0. Notably, numerous instances of reactivated parts from the most recent landslides were identified within the study area. Examples include the Vinohrady n. Váhom village – Kamenica landslides, Paradič (Figs. 13 and 14).
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Conclusions
The final degrees of stability computed for individual cells within the GIS environment should be considered holistically, treating them as components of a unified unit rather than isolated entities. Similar to the comprehensive approach taken in generating the final landslide hazard map, the aggregated degree of stability is most effectively assessed when subjected to various instability scenarios for internal comparisons. However, caution must be exercised in comparing these values with those derived from different modeling approaches.
The final landslide hazard maps, crafted from distinct input interpolated maps, exhibit notable disparities. The critical phase in landslide hazard assessment lies in data collection and the preparation of input maps. The selection of interpolation methods, along with their precise settings in the GIS environment, introduces a degree of subjectivity and potential error into the preparation of input parametric maps. While the application of multiple interpolation methods aims to mitigate this subjectivity, the output maps, used to compile “partial” landslide hazard maps, eventually contribute to the creation of final hazard maps for various model scenarios.
Deterministic analyses prove valuable in estimating the stability of the modeled area, particularly for the youngest generation of slope deformation involving shallow landslides with a slip surface depth of 5 m. The activation of shallow landslides e.g. in Vinohrady nad Váhom village in 2011, which posed a threat to local roads and family houses, underscores the importance of this analysis.
Despite the absence of these “new” landslides in the maps of registered landslides used for comparison, their localization in zones with stability less than 1.0 becomes evident when compared with the final hazard maps. To assess the effectiveness of these final maps, the stability calculation of selected profiles serves as a more appropriate way.
Comparative analyses involve bivariate and deterministic results, focusing on the percentage frequency of adverse classes in hazard maps. Notably, the comparison considers the class with the lowest stability degree (FS < 1) from the landslide hazard map for partially and fully saturated slopes. This is juxtaposed against the class indicating very high hazard in a map compiled through bivariate analysis using parameter weights. The high hazard level encompasses nearly 90% of the area with a factor of safety less than 1.0, with instability concentrated primarily at the slopes between Nitrianska pahorkatina Upland and the alluvial plain of the river Váh.
This comprehensive analysis offers valuable insights also for decision-makers in land-use planning and risk mitigation, emphasizing consistently identified unstable areas under various conditions.
Acknowledgements
This research was funded by Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic, VEGA, grant project No. 1/0182/23 and project APVV-21-0159.
Declarations
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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