## 3 Case Example  
Cantilever walls rely on their own weight to resist sliding and overturning, but they also benefit from the weight of the backfill above the heel of the wall. The reinforced concrete cantilever walls come with various geometries. They are much cheaper to erect than the gravity wall, so they can be prefabricated and transferred to the site directly. Sliding as one of the potential modes of collapse must always be considered in reliability designs. The minimum safety factor against sliding is considered to be equal to 1.5. The most significant sliding force component usually comes from the lateral earth pressure acting on the wall's active (backfill) side. Such force may be intensified by the presence of vertical or horizontal loads on the backfill surface. Figure 1 depicts the geometry of the cantilever wall as well as the major variables considered in this article. The safety factor against sliding can be indicated by the following in which \(F_{R}\) is the sum of the horizontal resisting forces, and \(F_{D}\) is the sum of the horizontal driving forces. \[FOS=\frac{\sum F_{R}}{\sum F_{D}}=\frac{\sum V\ tan\delta+1.4\ c+P_{p}}{P_{a} cos(i)} \tag{5}\]  
where \(\sum V\) is the sum of the total vertical forces acting. \(P_{a}\) and \(P_{p}\) are the active and passive rankin pressure, respectively. The following equations are used to calculate the active and passive pressure  
\[P_{p}=\frac{1}{2}\times K_{p}\times\gamma\times 1^{2},\ \text{where}\ K_{p}=\frac{ cosi+\sqrt{\left(cosi\right)^{2}-\left(cos\phi\right)^{2}}}{cosi-\sqrt{ \left(cosi\right)^{2}-\left(cos\phi\right)^{2}}}. \tag{6}\]  
\[P_{a}=\frac{1}{2}\times K_{a}\times\gamma\times 6.2^{2},\ \text{where}\ K_{a}=\frac{ cosi-\sqrt{\left(cosi\right)^{2}-\left(cos\phi\right)^{2}}}{cosi+\sqrt{ \left(cosi\right)^{2}-\left(cos\phi\right)^{2}}}. \tag{7}\]As illustrated in Figure 1, the soil profile behind the retaining wall is considered to have a slope of \(i=20^{\circ}\), which is considered in the calculation of the soil mass in the above equations. Moreover, \(c\) is the cohesion value, \(\phi\) is the angle of shearing resistance, and \(\delta\) represents the angle of wall friction (\(\delta=2/3\)\(\phi\)). In order to calculate all the datasets, the above-mentioned formulation has been scripted in MATLAB code to evaluate the FOS for various combinations of input variables. This study has a lot to contribute both to the field of AI and geotechnical engineering. This research work results from various new techniques in the market of evolving machine learning being employed in different research fields of medication and technical engineering. Cohesion (\(c\)), angle of shearing resistance (\(\phi\)), angle of wall friction (\(\delta\)), and unit weight (\(\gamma\)) were taken as primary variables, following a lognormal distribution function. For this study of retaining walls, data were collected, and the Coefficient Of Variation (COV) values were taken from different previous studies [39; 40]. The COV values for \(\phi\) and \(\delta\) are considered to be equal to 15%, while the mean value of 30\({}^{\circ}\) and 20\({}^{\circ}\) is applied, respectively. The random parameter of cohesion is assumed to have a mean value of 20 kPa. The fourth material parameter that is considered a random variable is the unit weight of soil mass \(\gamma\) with a mean value of 20 kN/m\({}^{3}\), and the COV is assumed to be equal to 8%. Afterwards, 80 datasets were generated randomly, of which 90% were put to training and 10% were put to testing. Three models--MARS, EmNN, and SOS--LSSVM--were used to predict the factor of safety. After modeling the problem, different assessments were done to analyze the performance of the three models. After that, the models were compared amongst each other using various error measurements. In addition, reliability analysis was done by calculating the reliability index using the FOSM method, which assumes that all the variables are independent.