# Prediction of Swelling Index Using Advanced Machine Learning Techniques for Cohesive Soils
###### Abstract  
Several attempts have been made for estimating the vital swelling index parameter conducted by the expensive and time-consuming Oedometer test. However, they have only focused on the neuron network neglecting other advanced methods that could have increased the predictive capability of models. In order to overcome this limitation, the current study aims to elaborate an alternative model for estimating the swelling index from geotechnical physical parameters. The reliability of the approach is tested through several advanced machine learning methods like Extreme Learning Machine, Deep Neural Network, Support Vector Regression, Random Forest, LASSO regression, Partial Least Square Regression, Ridge Regression, Kernel Ridge, Stepwise Regression, Least Square Regression, and genetic Programing. These methods have been applied for modeling samples consisting of 875 Oedometer tests. Firstly, principal component analysis, Gamma test, and forward selection are utilized to reduce the input variable numbers. Afterward, the advanced techniques have been applied for modeling the proposed optimal inputs, and their accuracy models were evaluated through six statistical indicators and using K-fold cross validation approach. The comparative study shows the efficiency of _FS-RF_ model. This elaborated model provided the most appropriate prediction, closest to the experimental values compared with other models and formulae proposed by the previous studies. s +
Footnote †: journal: Applied Sciences  
1  
have been among the major obstacles for research, dissemination, and implementation of soil mechanics in engineering practice [4]. Furthermore, classical constitutive modelling based on the elasticity and plasticity theories has a limited ability to correctly simulate the real behavior of soils. This is attributed to reasons associated with the complexity of soil formation and its heterogeneity [7]. For these reasons, geotechnical researchers have tried to develop new safe economical models using systems influenced by many factors, like the technical, economic, environmental, and geometrical parameters. These systems are called, all together, Artificial Intelligence (AI) or Machine Learning (ML). Many papers have been published in order to derive a different relationship and advanced models between the compression index (\(C_{c}\)) and the basic soil properties [6; 8; 9; 10; 11]. However, only a few widely accepted empirical equations have been proposed in the literature to estimate the swelling index (\(C_{s}\)) from physical soil parameters, such as the natural water content (\(W\)), the plasticity index (\(PI\)), the liquid limit (\(WL\)), the specific gravity, and others. Table 1 summarizes some proposed formulae for estimating \(C_{s}\). However, major shortcomings have been observed. The large amount of correlations published with respect to the same parameters point to an inherent variability of its usage. Therefore, the application of correlation analysis in other conditions or sites could yield incorrect results [12; 13]. In addition, these approaches generally depend on simplified assumptions, such as a linear behavior or production heuristics, which make regression analysis methods less effective when they are used for simulating the complex heterogeneous behavior of soil [14; 15; 16; 17]. On the other hand, the use of the \(ANN\) method in geotechnical engineering has witnessed a major development since the early nineties [21]. Several attempts using neural networks have led to impressive results. Between the important research works dealing with the swelling of soil, [PERSON] has utilized one hidden layer of the \(ANN\) model by analyzing a database consisting of 42 test data for fine-grained soil. The selected input parameters included the initial void ratio (\(e_{0}\)) and \(W\). The (2-8-1) \(ANN\) model (meaning two inputs, eight nodes in the hidden layer and one output) efficiently predicted \(C_{s}\)[20]. [PERSON] et al.