## 3 FEM Simulation and Data Collection  
### FEM Simulation  
In this study, eight different soil types were used along with significant diversity in their main attributes. These attributes can address almost the most usual kinds of sands. In the modelling, internal friction and dilation angles in the range of 32-42 and 3.4-11.5 degrees are selected and also utilized, respectively. Moreover, the elastic modulus, Poisson's ratio, and unit weight varied between the values of 17500-65000 kN/m\({}^{2}\), 0.333-0.249, and 19-21.1 kN/m\({}^{3}\), respectively. The soil properties, which are attended for prediction of a network can be shown as a series of the graphical summary that is the range of input data. These datasets include friction angle, Poisson's ratio, elastic modulus, and unit weight is drawn in Figure 6. To determine applied stresses beneath the footing (F\({}_{\rm{ult}}\)), asymmetric FEM of circular foundation, for example, a width around 1.0 m is placed on two-layer soils (Figure 7). Infeasible civil engineering plans, the layers of soil beneath the foundations are not homogeneous, commonly, and there are many cases where (i) a weaker soil layer rested on a stronger soil layer or (ii) stronger soil placed on a soil layer with much weaker physical characteristics. Plaxis 2D (a commercial finite element software) is employed to predict the influences of soil layer's properties on ultimately  
Figure 5: The flowchart of the ICA process (after [PERSON] and [PERSON] [49]).  
applied stresses. Based on several recommendations (e.g., [PERSON] and [PERSON] (2018), and [PERSON], et al. (2019)) the most effective factors, which influence the maximum bearing capacity of the soil, are (i) soil properties (for example, soil layer thickness beneath the footing), maximum expected settlement (s), friction angle \(\varphi\), unit weight \(\gamma\), elastic modulus E, Poisson's ratio \(\upsilon\), type of design analysis, and dilation angle \(\psi\). (Table 1). Note that, in the present work, cohesion has been considered equal to zero for estimating the F\({}_{\text{ult}}\) in distinct layered sandy soils. In addition, zero value for cohesion means soil does not have any cohesive strength and provides sandy soil state. Values of 0, 0.4, 0.4, 0.8, and also 1.0 are selected for the upper layer width of thickness.  
Figure 6: A summary of the range of input information vs. soil type, (**a**) Dilation angle, (**b**) Unit weight, (**c**), Internal friction angle, (**d**) Elastic modulus, (**e**) Poisson’s ratio  
As stated earlier, to generate the best structure for the proposed hybrid models, the database employed to train the models is obtained by a total of 3513 full-scale finite element simulations. The dataset is considered for a circular footing with a radius of 1.0 m, rested on two-layered soil condition. It is noted that the vertical stress amounts before arriving at the maximum S/B ratio are labelled Fult-Based on many similar works (e.g., Anvari and Shooshpasha [52] and [PERSON] and Manavirad [53]), soil layer thickness beneath the footing, maximum expected settlement (s), friction angle \(\varphi\), unit weight \(\gamma\), elastic modulus E, Poisson's ratio \(\upsilon\), type of design analysis, and dilation angle \(\psi\) were selected as inputs and applied datasets for building the proposed models. An instance of a database received by the FEM simulation and effective factors influencing the Fult, as the model output, selected in the ANN algorithm was shown in Table 2.