## 1 Introduction  
The modern world could not function without the raw materials produced by the mining industry. As the demand for mineral products is increasing, mining produces vast amounts [1]--of the order of billion tons yearly--of various types of mining waste [2], including tailings. These are mixtures of crushed rock and processing fluids from mills, washeries or concentrators that remain after the extraction of the economic metals, minerals, mineral fuels or coal [3]. The tailings are usually stored under water in order to prevent the formation of surface dusts and acid. There are several approaches towards the handling and storage of tailings (i.e., submarine or riverine disposal, wetland retention, backfilling), but the main method currently used is their storage behind dammed impoundments, with the resulting structures termed \"tailings ponds\" or \"tailings dams\" (TP/TD). The creation and management of these structures is a process that begins in the early stages of a mining operation but is continued throughout the mine's life until its closure and beyond (post-closure), with the main objective being to safely store tailings and reduce the risks over the long term [4; 5; 6]. There are a large number of recorded failures of tailing ponds present in the literature [7; 8; 9; 10], and most of them produced severe environmental damage and/or loss of human life. Several scholars, notably [PERSON] [11], [PERSON] et al. [12; 13] reviewed the causes and mechanisms leading to TP/TD failures, and categorized them as physical/structural, functional or environmental, each with several subcategories [14; 15]. These failures are not usually produced by a single factor, but rather are the result of multiple factors acting together [16]. Most of the time, the influence of the external environment (earthquakes, rainfall, flooding, dam foundation subsidence, etc.,) cause changes in the stress and seepage fields, leading to the destabilization of the structure. The most frequent causes of failure were determined to be linked with groundwater level and its influence on dam foundation-soil permeability [17; 18], the erosion produced by heavy rainfalls [19; 20; 21; 22], seismic activity [23; 24; 25]; all of these causes leading to failure of the dam's slope due to weakened and liquefied underlying layers, overtopping of the liquefied material, and an increase in lateral pressure on the dams. In order to prevent these situations, engineers developed several procedures and tools that can be used to assess the stability of TP/TD. Stability analysis methods play a crucial role in ensuring the safety and reliability of these structures [26]. By utilizing advanced techniques and software, engineers are able to assess factors such as the critical slip surface of slopes, plastic zone distribution, deformation characteristics of slopes, and factor of safety (FOS). Various methods are used for determining the FOS of TP/TD using different approaches and tools. First, there are conventional analytical approaches based on the limit equilibrium methods (LEM) [27], with multiple techniques belonging to LEM: Swedish slip circle, ordinary method of slices, i.e., Bishop, Morgenstern-Price, Spencer, Janbu, Fredlund, etc., [28; 29; 30; 31; 32] which usually establish very conservative and safe estimations of FOS due to their simplification assumptions. These methods have been used for several decades and proven to be effective in many practical engineering problems. Next, there are more modern approaches for assessing the safety of TP/TD including cloud model analysis [33], set pair analysis [34; 35], or fuzzy logic [36; 37]. Finally, there are the numerical methods of analysis [38; 39; 40]. As computer performance and processing power have increased in recent years, these have allowed the simulation of problems which otherwise were too complex for conventional methods, because of complex geometry, material anisotropy, nonlinear behavior, in situ stresses, etc.