## 1 Introduction
The initial hydraulic conductivity is decreased by 30% and 45%, respectively, with the addition of 2% nano \(\gamma\)-Al\({}_{2}\)O\({}_{3}\) and 2% nano CuO [28]. [PERSON] and [PERSON] report that the hydraulic conductivity value of pure soil sample decreased from 2.16 \(\times\) 10\({}^{-9}\) m/s to 9.46 \(\times\) 10\({}^{-10}\) m/s and 7.44 \(\times\) 10\({}^{-10}\) m/s, respectively, with the addition of multiwall carbon nanotube (CNT) and carbon nanofiber (CNF) [29]. [PERSON] et al. investigate the effect of nanosilica particles of two different sizes, 15 nm, and 80 nm, on the hydraulic conductivity of the soil. Nanosilica particles with the size of 15 nm further reduced the hydraulic conductivity. [PERSON] attributes this to the fact that the packing density of smaller-sized nanoparticles is higher than that of larger-sized nanoparticles [30]. There are many machine learning studies on permeability estimation in the literature. [PERSON] et al. make an estimation of permeability using Evolutionary Polynomial Regression; the obtained results are compared with the Artificial Neural Networks and better results are obtained [31]. In [PERSON] and [PERSON]'s studies, permeability estimation is made using ANN and comparative analyses are made with previous Artificial Neural Networks studies [32]. [PERSON] et al. calculate the compaction parameters related to permeability using the Support Vector Machine model [33]. In [PERSON] and [PERSON]'s study, Support Vector Machine and decision trees are used to calculate compaction parameters. The Support Vector Machine model is found to produce better results [34]. On the other hand, [PERSON] et al. hypothesize that Support Vector Machines, Multi Linear Regression, Genetic Programming, and Random Forest algorithms are used for permeability estimation. The Support Vector Machine model has been found to produce the best results [35]. [PERSON] and [PERSON]'s study is intended to develop correlations between permeability and different soil properties using the Multi Linear Regression method [36]. [PERSON] et al. 's study is aimed to create a permeability-predicting ANN structure by using different ANN structures. The obtained results are compared with MLR and it is seen that ANN produced better results [37]. In another study, permeability, maximum dry density (MDD), and optimum moisture content are estimated using ANN. The obtained results are compared with Statistical Equations and it is seen that ANN is a suitable model [38]. [PERSON] et al. present artificial neural network prediction models, which relate compaction characteristics, permeability, and soil shear strength to soil index properties. A comparison of the results demonstrates that the developed ANN models provide highly accurate predictions [39]. Finally, [PERSON] and [PERSON]'s research predicts the permeability of loosely packed granular materials is made using ANN and MLR. One can see that ANN gives the best results [40]. This study is aimed to improve the impermeability of the base by adding different percentages of aluminum oxide and iron oxide as nanomaterials into the kaolin sample. 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. Thus, the Flow Resistance (FR) model is employed for the first time to approach this problem with an analogy of the typical traffic flow phenomenon. Finally, the obtained data are evaluated and the drawn conclusions are discussed.