This article presents several reasonable cases in which four mechanisms - dissolution, physical mixing, adsorption, and precipitation (either chemical change or evaporation) - might concentrate fissile material in and around a disposal container for radioactive waste at the proposed repository at Yucca Mountain, Nevada. The possible masses, concentrations, and volume are then compared to criticality limits. The cases examined evaluate the geologic barrier role in preventing criticality since engineered options for preventing criticality (e.g., boron or gadolinium neutron absorber in the disposal container) are not considered. The solid concentrations able to form in the natural environment are insufficient for criticality to occur because (a) solutions of 235U and 239Pu are clearly not critical; (b) physical mixing of fissile material with the entire potential iron oxide (as goethite - FeOOH) in a waste package is not critical; (c) the adsorption of 239Pu on consolidated iron oxide in a waste package is not critical; (d) the adsorption of 235U on consolidated iron oxide in a waste package is not critical when accounting for reduced adsorption because of carbonates at high pH; (e) the filtration of iron oxide colloids, containing fissile material, by the thin invert material is not critical; (f) insufficient retention through precipitation of 235U or 239Pu occurs in the invert; (g) adsorption of 235U and 239Pu on devitrified or clinoptolite-rich tuff below the repository is not critical; (h) the average precipitation/adsorption of 235U as uranyl silicates in the tuff is not critical by analogy with calcite deposition in lithophysae at Yucca Mountain; and (i) precipitation/adsorption (caused by cyclic drying) as uranyl silicates on fracture surfaces of the tuff is not critical by analogy with the oxidation of UO2, migration of UVI, and precipitation in fractures at the Nopal I ore deposit in Mexico.