## 1 Introduction  
Landfilling, one of the final disposal methods for solid waste, is the most used method worldwide [1]. Control of leachate generated in landfills is of great importance for the environment and human health. The use of soil with low permeability in a landfill prevents leachate contaminants from easily leaking from the ground and mixing with groundwater [2, 3]. Clayey soils are widely used in landfill areas due to their low permeability [4]. However, the properties of the clay change as a result of interactions such as cation exchange, dissolution/precipitation, and redox reactions between the clay and leachate [5]. It has been reported by many researchers that pH [6], salt solutions [7, 8], organic matter [9, 10], and heavy metals [9, 11, 12] increase the permeability of clayery liners used in landfills. The resulting increase in permeability raises great concern about the environmental fate of leachate pollutants such as heavy metals. Heavy metals are defined as metals with a density higher than 5 g/cm\({}^{3}\), and heavy metals include iron (Fe), manganese (Mn), zinc (Zn), lead (Pb), copper (Cu), arsenic (As), cobalt (Co), nickel (Ni) [13, 14]. Electronic devices, batteries, pesticides, fertilizers, paints, and varnishes in the landfill are among the materials that increase heavy metal content [15, 16, 17]. Heavy metals are highly threatening pollutants due to their persistence, non-degradability, and toxicity [18]. Clays have high specific surface areas and small particle sizes that increase chemical and physical interaction with heavy metals [17]. [PERSON] et al. reported that Cd\({}^{2+}\), Cr\({}^{3+}\), Pb\({}^{2+}\) and Ni\({}^{2+}\) heavy metals in leachate can be adsorbed more strongly in clay loamy texture than in loamy sand textured soil [19]. The voids of soils vary from micrometer to nanometer [20]. Filling the voids of clayey soils with nanomaterials changes the permeability. Studies have been carried out to reduce the permeability and/or hydraulic conductivity of soils by using different nanosized materials by many researchers. [PERSON] et al. investigated the changes in the properties and permeability of clayey soil resulting from the addition of nano clay with high aspect ratio and good thermal and physical properties. [PERSON] et al. reported that soil permeability decreased from 3 \(\times\) 10\({}^{-9}\) cm/s to 9.4 \(\times\) 10\({}^{-11}\) cm/s with the addition of 3% nano clay to clay soil [21]. [PERSON] and [PERSON] added nano gamma-aluminum oxide (\(\gamma\)-Al\({}_{2}\)O\({}_{3}\)) and nano copper oxide (CuO) into kaolin clay because they are insoluble in water and chemically stable, and investigated the changes in the properties and hydraulic conductivity of kaolin clay. [PERSON] and [PERSON] reported that the pores of kaolin clay were clogged with the addition of \(\gamma\)-Al\({}_{2}\)O\({}_{3}\) and nano CuO, and the hydraulic conductivity decreased by 30% and 45%, respectively, with the addition of 2% \(\gamma\)-Al\({}_{2}\)O\({}_{3}\) and CuO into kaolin clay [22]. [PERSON] et al. added 1-8% nano clay to kaolinite in order to improve the hydraulic properties of kaolinite. Kaolinite was investigated concerning the effect on the permeability coefficient of nano clay addition of up to 8%, and it was found that the permeability decreased gradually with increasing nano clay content. The experimental results showed that the addition of 8% nano clay to kaolinite reduced the permeability coefficient by 300 times [23]. [PERSON] et al. carried out a study to find the appropriate nanoparticle concentration for reducing the permeability of clay soils of zero-valent nano iron particles, which have lower costs and lower toxicity than other metallic nanoparticles. In the study by [PERSON] et al., the changes in the hydraulic conductivity of clay soil in suspensions with different concentrations nano iron varying in the range of 1-10 g/L were investigated.