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This paper presents the physical stability analysis of three types of cover systems with geomembrane and geosynthetic clay liner that could be placed in the closure of tailings and mine waste storage facilities and heap leach pads. The physical stability of these cover systems was analyzed considering the reinforcement with geogrids and geocells and the effects of seismic and seepage forces. The reinforcement force was estimated considering the strain compatibility in a composite column model. The shear strength parameters of interfaces between geosynthetics and adjacent materials were estimated by large scale direct shear tests carried out at low normal stress (<50 kPa). A parametric study was performed previously to illustrate the sensitivity of the factor of safety to the most important design parameters. Subsequently, multiple scenarios have been analyzed considering different geometric configurations, seismic and seepage buildup conditions, types of reinforcement, failure surfaces above and up the liner, etc. Then, a matrix based on this analysis is proposed. The necessary conditions for the stability of the cover systems analyzed are indicated in this matrix. This study was complemented with a probabilistic analysis based on reliability theory using the Monte Carlo simulation method to take into account the variability in the design parameters. Finally, design charts with reliability indexes are also proposed which will be useful for preliminary designs of cover systems in mining projects.