The tailings from gold beneficiation can cause various negative impacts, necessitating measures to prevent their transport and environmental contamination. Geomembranes serve as hydraulic barriers in mining tailings reservoirs, thereby supporting the Sustainable Development Goals (SDGs). To ensure that the geomembrane effectively mitigates environmental impact, it is essential to study its durability when applied in the field. This article examines the long-term performance of an HDPE geomembrane exposed for 7 and 11 years at a gold mining tailing site in Brazil. Samples were exhumed from different locations at the dam, and their properties were evaluated. Non-parametric statistics were employed using the Kernel Density Estimator (KDE). For the 11-year-old geomembranes, the probability of the geomembrane reaching nominal failure in terms of tensile strength was 0.4%. The peel separation values exceeded the maximum allowable by the GRI GM13 standard. Although the geomembranes showed significant antioxidant depletion, suggesting they were close to or had already reached their residual stages, they approached nominal failure based on their stress crack resistance but did not rupture. The environmental analysis indicated no significant contamination in the area, corroborating that the geomembrane is fulfilling its function. The non-parametric methodology proved promising for durability analysis and could be applied to other engineering projects with geosynthetics, thereby adding reliability to decision-making in alignment with sustainable development.