## 1 Introduction  
The disposal of solid wastes by landfill is a more widely used disposal method compared to others due to its economic advantages and simplicity [1]. With the effect of water in the composition of the wastes, precipitation, and physical, chemical, and biological reactions, leachate occurs in landfill areas [2]. Leachate is wastewater with a high contaminant content that contains organic substances, monovalent and multivalent ions, microorganisms, and heavy metals [3]. The type of waste in the landfill, waste composition, age of the landfill and climatic conditions are all factors that affect the chemical composition of the leachate [4]. In typical leachate, the chemical oxygen demand (COD), total phosphorus (TP) concentration, and organic nitrogen concentration vary in the range of 140-152,000 mg/L, 0.1-30 mg/L, and 14-2500 mg/L, respectively [5, 6, 7]. Liners with low hydraulic conductivity (\(k\leq 10^{-7}\) cm/s) are used to prevent leachate from reaching the groundwater in landfill areas. Hydraulic conductivity depends on many factors such as the void ratio, medium porosity, pore size, soil type, liquid type, and contaminant concentration [8; 9]. As the leachate passes through the clayey soil, it causes changes in the structure and properties of the clay, resulting in an increase or decrease in hydraulic conductivity. The increase in ion concentration [10; 11], ionic valence [12; 13], and organic matter concentration [14; 15] in the leachate contributes to increasing the hydraulic conductivity, while the increase in the number of microorganisms [16] and the suspended solid concentration [17] contributes to the decrease in hydraulic conductivity. The increase in hydraulic conductivity as a result of the leachate-liner interaction is caused by factors such as the thinning of the diffuse double layer (DDL) thickness of the clay, agglomeration, flocculation of the clay particles, the formation of cracks in the soil structure, and the increase in the void ratio [12; 14; 18; 19]. The low permeability of the liner, which can be provided with natural materials such as clay, is of great importance in terms of not polluting the groundwater with the leachate of the landfill area. However, geomembranes are used alongside the low permeability liner when the landfill area is inclined. The use of clay in landfills is more advantageous and preferable due to the cost of geomembranes and the risk of puncture. Therefore, it is important to improve the permeability of clay with nanomaterials [20; 21]. The properties of the clays used in the landfill can be modified by adding nanomaterials to the clay. The high specific surface area of nanoparticles can cause a high surface energy between the particles, which can greatly change the engineering properties as well as the physical and chemical properties of the soil [22; 23; 24]. For instance, [PERSON] et al. state that the addition of nano MgO and nano Al\({}_{2}\)O\({}_{3}\) into kaolinite clay resulted in a decrease in the liquid limit, plasticity limit, plastic index, and swelling potential of the soil [25]. In addition, the presence of nanoparticles in the clay, and the increase in nanoparticle concentration, change the bonding and adhesion between the clay particles, increase the connection between the pores and cause the number and size of the pores to decrease [23; 24; 26]. Increasing the soil integrity of the clayey soil and decreasing the porosity through nanomaterials cause a decrease in hydraulic conductivity. Studies in the literature reveal that nanomaterial type [27; 28; 29], concentration [28; 29], and size [30] affect permeability. [PERSON] et al. report that the permeability coefficient decreased from 2.41 \(\times\) 10\({}^{-5}\) cm/s to 1.25 \(\times\) 10\({}^{-5}\) cm/s as a result of filling the soil voids with the addition of nano CaO to clayey soil [27]. [PERSON] and Coo mix two different nanomaterials, gamma-aluminum oxide (\(\gamma\)-Al\({}_{2}\)O\({}_{3}\)) and nano-copper oxide (CuO), with kaolin clay in different proportions.