## 2 Materials and Methods
### Experimental Design  
Numerical simulations were carried out using the previously described geotechnical model. Two input groups can be considered in this model, grouped according to soil and slope geometry properties. Among the soil factors are strength parameters--cohesion (_c_) and friction angle (\(\phi\)), and the soil state parameters--unit weight, \(\gamma\) The geometry factors are slope height (\(H\)) and slope angle (\(\beta\)). To perform a regional sensitivity analysis (RSA), [PERSON] et al. [56] suggested a number of simulations between 100 \(\times\) M and 1000 \(\times\) M, where M is the number of model inputs. This study includes five input factors (cohesion, friction angle, unit weight, slope height, and slope angle). First, 1000 simulations were carried out, and the convergence of the results was studied; however, as no convergence was observed, the number of simulations was increased to 5000. Convergence of the results was verified for 5000 simulations; therefore, these simulations were used for all the analyses. The model simulation was carried out through Monte Carlo simulations, assuming for each input parameter the ranges presented in Table 1, which correspond to the typical values of the different parameters for the studied soil type found in the literature. Parameter values were generated assuming that they are independent and with a uniform probability distribution for all parameters used. Slope height depends on the project; it is defined in the slope design and limited by the design requirements, the technical equipment available for construction, and the project budget. Thus, slopes with various heights can be found. In this study, the analyzed slope height range was limited to between 2 and 30 m. According to Chilean regulations for highway slope construction [59], slopes must have a maximum inclination between 26\({}^{\circ}\) and 56\({}^{\circ}\); however, [PERSON] [60] stated that residual soil slopes can be stable even at 60\({}^{\circ}\). Therefore, the slope inclination range for the present analysis was defined as between 26\({}^{\circ}\) and 80\({}^{\circ}\) in order to include cases of instability in the analysis and simulations. [PERSON] [61], [PERSON] [62], and [PERSON] [63] characterized and described residual granite soils in Chile, Portugal, and Hong Kong, respectively. Based on these studies, soil strength parameters range from 0 to 5 kPa for the cohesion values of this type of soil and the friction angle varies between 29.5\({}^{\circ}\) and 38.0\({}^{\circ}\). It bears mentioning that there are cohesion results greater than 5 kPa in the works of other authors (such as [62; 64]). Chilean maicillo is normally classified as silty sand according to the Unified Soil Classification System (ASTM D2487-17). Thus, greater cohesion values are considered excessive, as they could correspond to a granite residual soil with a greater degree of weathering than the studied material. Based on the work of [PERSON] [64], in which a geomechanical characterization of the granite residual soil of the Cordillera de Nahuelbuta range in Chile was carried out, a range of 17 to 21 kN/m\({}^{3}\) was defined for the unit weight. The shear strength reduction method (SSRM) was implemented in the finite element-based geotechnical calculation software OptumG2 2021(r) (Optum Computational Engineering, Copenhagen, Denmark). This program allows the geometric and geomechanical conditions of the slope to be modified and its files to be executed based on external programming codes. To this end, a code in the Python programming language ([[https://www.python.org](https://www.python.org)]([https://www.python.org](https://www.python.org)), accessed on 19 January 2022) was developed, allowing Monte Carlo simulations to be configured, run, and the obtained results to be saved. The processing of the results was carried out using the SAFE (Sensitivity Analysis For Everybody) Toolbox published by [PERSON] et al. [65] in its Python version.