## 1 Introduction  
Tailings dams are earth dams without an impermeable core, designed for permanent containment of mineral waste. One of the most used construction methods is the upstream method, by which the dam banks grow during the tailing's storage activity at a rate of about 1-1.5 m/year. This method is the most cost-effective [1, 2], as it consists in the construction of a foundation base very resistant to load and of the so-called starter dam, then the tailings are discharged into the basin until it is saturated and the placing of the new material occurs within the existing impoundment, that is, the new embankments are founded on tailings [3, 4]. These latter ones consist of solid or liquid waste represented by a mixture of fine particles, in some cases toxic or radioactive, deriving from mechanical separation processes of the mineral of economic interest from the gauge. As its height and therefore the load increases, this kind of dam is more susceptible to geotechnical failure, or it can evolve in conditions of instability, as the new embankmentsare founded on tailings, which are in most cases highly erodible due to their fine particle size and can contain unwanted minerals and process chemicals [5]. In the past 20 years, the number of tailings dam failures has doubled [6] with dramatic consequences due to the toxicity of the stored tailings and the large run-out distances (up to hundreds of km), causing losses and major damage to health and environment. An upward trend in high-consequence failure events since 1990 has been also highlighted by [PERSON] and [PERSON] [7]. [PERSON] and [PERSON] [8] summarized the major tailings dam failures from 1910 to 2010, reporting that the annual failure frequency for major tailings dams is about 0.12%, which is more than two orders of magnitude greater than the annual failure frequency for large water retention dams [9]. Major failures occur with a frequency that ranges from two to five times per year, whereas minor failures occur around 35 times per year [10]. The most common result of failure is bursting of the dam which surrounds the facility and release of a huge mass of liquefied tailings mixed with water in the form of a flood wave. [PERSON] and [PERSON] [10] and [PERSON] and [PERSON] [7] described some examples of the over 100 documented catastrophic failures of tailings dams in the world over the last 50 and 100 years, respectively, and [PERSON] et al. [4] conducted a study on 147 cases of tailings dam failures worldwide, 26 of which had occurred in Europe. The most important causes of failure described on literature are the following: issues related to foundations, slope instability, overfilled tailings pond, mine subsidence or deformations of the dam body, unusual heavy rainfall, water pressure excess in tailings, piping/seepage, seismic liquefaction caused by earthquakes, structural issues, management, or operational errors. In many cases, no single precise cause for the failures has been identified, and various overlapping factors could combine [10]. [PERSON] et al. [2] also summarized the influence of the failure height, the building type, the geographical location, and time distribution of the tailings dam failures, and interestingly highlighted that upstream dams have a high probability (58%) of damage, and that the majority (85%) of tailings dam failures have occurred in dams of less than 45 m high. On 5 November 2015, Samarco's tailings dam breached, destroying two villages, killing 19 people, and seriously polluting 650 km of the Rio Docc River in the Brazilian state of Minas Gerais. In the same state, and with the same mine owner, in January 2019, the Corrego do Feijio dam at Brumadinho collapsed, killing about 248 people. The 86 m height tailings dam, constructed with the upstream method, catastrophically failed, releasing 12 million m\({}^{3}\) of mineral waste.