Impermeable base layers that are made of materials with low permeability, such as clay soil, are necessary to prevent leachate in landfills from harming the environment. However, over time, the permeability of the clay soil changes. Therefore, to reduce and minimize the risk, the permeability-related characteristics of the base layers must be improved. Thus, this study aims to serve this purpose by experimentally investigating the effects of nanomaterial addition (aluminum oxide, iron oxide) into kaolin samples. The obtained samples are prepared by applying standard compaction, and the permeability of the soil sample is experimentally investigated by passing leachate from the reactors, in which these samples are placed. Therefore, Flow Resistance (FR) analysis is conducted and the obtained results show that the Al additives are more successful than the Fe additive in reducing leachate permeability. Besides, the concentration values of some polluting parameters (Chemical Oxygen Demand (COD), Total Kjeldahl Nitrogen (TKN), and Total Phosphorus (TP)) at the inlet and outlet of the reactors are analyzed. Three different models (Artificial Neural Networks (ANN), Multiple Linear Regression (MLR), Support Vector Machine (SVM)) are applied to the data obtained from the experimental study. The results have shown that polluting parameters produce high FR regression similarity rates (>75%), TKN, TP, and COD features are highly correlated with the FR value (>60%) and the most successful method is found to be the SVM model.