The Return Period of Rainfall-induced Static Liquefaction of Tailings Dams

A modelling study

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Tailings are the rock flour which result from the process of mineral extraction at a mine. This waste material is stored in tailings storage facilities, also known as tailings impoundments. These impound­ments gradually grow in size during operation as more tailings are produced and stored over time. These structures are however also prone to failure. Well known failures in the past years are that of the Feijão and Fundão dams in the Minais Gerais state in Brazil. Static liquefaction of the dams has caused mud­streams in which many people were killed and the environment became heavily polluted. This study researched the probability of rainfall­-induced static liquefaction, as meteorological causes have often been named the trigger of failure. The study was limited to upstream raised decommissioned dams in the Minas Gerais state in Brazil. An analysis methodology was established in which the needed rainfall intensity to failure was calculated for different durations of rainfall. In a geohydrological analysis, the Richards equation for unsaturated flow was solved, to model rainfall infiltration. A quasi­-2D procedure was implemented to allow for a computationally efficient solution. Following the results of the geohydrological analysis, a limit equi­librium method was employed to calculate the factor of safety against liquefaction of the dam. In this case, the undrained strength analysis was applied together with an effective stress analysis to model both liquefiable tailings and non­liquefiable tailings in the tailings storage facility. If the factor of safety was equal to a predefined factor of safety associated with failure, the failure intensity was found. The failure intensity was converted to a return period of failure by the application of the Gumbel distributions that are part of the intensity­-duration­-frequency curve of rainfall. These IDF­-curves describe for all possible combinations of intensity and duration the probability of occurrence. Integration of the IDF­-curve for the failure intensities yields the total return period of failure as a single perfor­mance indicator. The analysis was restricted to a period of 5 days of continuous rainfall (storm events) as evaporation effects were not considered and no longer rainfall events were observed in the precipi­tation data used. A series of sensitivity studies was performed to observe how rainfall influences the stability of a tailings dam. It was found that failure is attributed to a loss of suction in the unsaturated zone upon rainfall in­ filtration as well as a loss of strength due to mounding of the water table. Because of the low strengths that liquefiable tailings have, there was the tendency to develop deep slip surfaces below the phreatic surface, causing only marginally stable dams to be prone to failure because of rainfall infiltration. The factor of safety upon rainfall is reduced in the order of 2 to 5 % depending on the parameters used. The strength parameters were of the largest influence. Increasing the friction angle of the non­-liquefiable tailings by 10 % increases the return period of failure by approximately 400 years. The strength ratios used to model the liquefiable tailings are of even larger influence. Adjusting that by only 2 % leads to a jump in the return period of failure of around 1000 years. The chosen boundary conditions for the phreatic surface in the impoundment were also of great influence. A difference of 0.3 meters for the water table for a dam of 20 meters high brings the dam to marginal stability. Given the little sensitivity to storm events, it is recommended to shift focus towards the behaviour of the phreatic surface over longer simulation periods to model the effect of e.g. extremely wet seasons. In addition, construction defects should be considered in which perched water tables could arise, severely decreasing the stability of a tailings dam.