## 2 Materials and Methods
### Sensitivity Analysis  
Sensitivity analysis methods allow the determination of how the variation of an output factor can be affected by the variation of the values of input factors or parameters of a numerical model [56]. [PERSON] et al. [56] described three elements present in sensitivity analysis methods: model, input factor(s), and output factor(s). A model is a mathematical procedure that simulates the behavior of a given system. Inputs are parameters, variables, and boundary conditions of the model, while outputs are the elements obtained after running the model. Scalar functions can be derived from the outputs (Equation (6)); they can be objective functions (performance calculated as the comparison of a model with observations) or prediction functions (scalar functions that represent a specific place or time). \[I\times\Omega=O \tag{6}\]  
Sensitivity analyses can be classified according to various criteria: variability (local or global), approach (quantitative or qualitative), sampling strategy (one at a time or all at once), and objective (screening, ranking, or mapping), such that an analysis method must  
Figure 2: Conceptual diagram of the geotechnical model of a slope. be adopted in accordance with the objective of the investigation. Thus, to determine the influence of geomechanical parameters and slope geometry on the safety factor, it must be ascertained which input factors have the greatest influence on the output factor (ranking) and in which variability space the influence occurs (mapping). According to the classification carried out by [PERSON] et al. [56], among the sensitivity analysis methods with the aforementioned characteristics are regional sensitivity analysis (RSA), correlation and regression methods, variance-based sensitivity analysis (VBSA), and density-based sensitivity analysis (DBSA). The regional sensitivity analysis (RSA) method allows the identification of regions in the input space associated with particular output values and permits mapping and ranking. Correlation and regression methods allow information on output sensitivity to be obtained by performing ranking or mapping, but not both at the same time. Due to their characteristics, variance-based methods (VBSA) allow screening and ranking based on the variance of output distributions. Methods based on density (DBSA) also allow screening and ranking, but unlike VBSA, they perform these tasks on the basis of variation of the probability density function (PDF) of the outputs. The regional sensitivity analysis method (RSA) [57; 58] allows regions of the input space associated with particular output values to be identified. [PERSON] et al. [56] added the classification of behavioral models (BM) and non-behavioral models (N-BM), differentiating them in accordance with a threshold or value defined for a previously defined performance measure or prediction function. The results of both groups can be graphed, and, via visual inspection of the cumulative distribution functions, spaces of each parameter that allow sensitivity to be determined or spaces with a positive or negative influence on outputs can be identified. Similarly, the difference between the cumulative distribution functions (CDF) of BM and N-BM measured by the Kolmogorov-Smirnov statistic is used as a measure or index of sensitivity of the model outputs to variations of the analyzed parameter (Equation (7)). \[S_{i}=max_{x_{i}}\big{|}F_{x_{i}|y_{b}}(x_{i}|y\in Y_{b})-F_{x_{i}|y_{mb}}(x_{ i}|y\in Y_{mb})\big{|} \tag{7}\]  
where \(F_{x_{i}|y_{b}}\) and \(F_{x_{i}|y_{mb}}\) are the empirical cumulative distribution functions \(x_{i}\) of the behavioral and non-behavioral input samples. This parameter is also known as the maximum vertical distance (mvd). These empirical functions provide a robust approximation of the underlying distribution, as in the case in which parameterizations are limited to sub-regions of the space.