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This study aims to use regression Least-Square Support Vector Machine (LS-SVM) as a probabilistic model to determine the factor of safety (FS) and probability of failure (PF) of anisotropic soil slopes.

This research uses machine learning (ML) techniques to predict soil slope failure. Due to the lack of analytical solutions for measuring FS and PF, it is more convenient to use surrogate models like probabilistic modeling, which is suitable for performing repetitive calculations to compute the effect of uncertainty on the anisotropic soil slope stability. The study first uses the Limit Equilibrium Method (LEM) based on a probabilistic evaluation over the Latin Hypercube Sampling (LHS) technique for two anisotropic soil slope profiles to assess FS and PF. Then, using one of the supervised methods of ML named LS-SVM, the outcomes (FS and PF) were compared to evaluate the efficiency of the LS-SVM method in predicting the stability of such complex soil slope profiles.

This method increases the computational performance of low-probability analysis significantly. The compared results by FS-PF plots show that the proposed method is valuable for analyzing complex slopes under different probabilistic distributions. Accordingly, to obtain a precise estimate of slope stability, all layers must be included in the probabilistic modeling in the LS-SVM method.

Combining LS-SVM and LEM offers a unique and innovative approach to address the anisotropic behavior of soil slope stability analysis. The initiative part of this paper is to evaluate the stability of an anisotropic soil slope based on one ML method, the Least-Square Support Vector Machine (LS-SVM). The soil slope is defined as complex because there are uncertainties in the slope profile characteristics transformed to LS-SVM. Consequently, several input parameters are effective in finding FS and PF as output parameters.

The purpose of this paper is to extend the scaled boundary radial point interpolation method (SBRPIM), as a novel semi-analytical scheme, to the analysis of the steady state confined seepage flows.

This method combines the advantages of the scaled boundary finite element method and the BRPIM. In this method, only boundary nodes are used, no fundamental solution of the problem is required, and as the shape functions constructed based on the RPIM satisfy the Kronecker delta function property, the boundary conditions of problems can be imposed accurately and easily.

Three numerical examples, including seepage flow through homogeneous and non-homogeneous soils, are analyzed in this paper. Comparing the flow net obtained by SBRPIM and other numerical methods confirms the ability of the proposed method in analyzing seepage flows. In addition, in these examples, the accuracy of the SBRPIM in modeling the velocity singularity at a sharp corner is illustrated. SBRPIM accurately models the singularity point in non-homogeneous and anisotropic soil.

SBRPIM method is a simple effective tool for analyzing various kinds of engineering problems. It is easy to implement for modeling the velocity singularity at a sharp corner. The proposed method accurately models the singularity point in non-homogeneous and anisotropic soil.