## 2 Materials and Methods
### Generation of Simulations  
The use of the sensitivity analysis method requires a large amount of data. In the case of this study, each of the points used in the analysis is the result of a numerical simulation using values in the ranges established by the Monte Carlo simulation as input parameters. Therefore, in this study, 5000 numerical simulations of slopes with different characteristics were generated and analyzed. A system that allows the creation of models and extraction of the results to be automated was used to obtain the results, making the project feasible. The methodology used to generate the models to be studied was implemented in Jupyter Notebooks ([[https://jupyter.org](https://jupyter.org)]([https://jupyter.org](https://jupyter.org)), accessed on 19 January 2022) using the Python kernel, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Height, \(H\) (m)** & **Slope Angle, \(\beta\) (\({}^{\circ}\))** & **Cohesion, \(c\) (kPa)** & **Friction Angle, \(\phi\)** & **Unit weight, \(\gamma\)** \\  & **(m)** & **(\({}^{\circ}\))** & **(kPa)** & **(\({}^{\circ}\))** & **(kN/m\({}^{3}\))** \\ \hline Range & 2–30 & 26–80 & 0–5 & 29.5–38 & 17–21 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Range of model parameters’ variation, assuming a uniform probability distribution. which allows a well-structured and replicable workflow and simplifies the interaction between the user and the developed software due to the internal organization of the notebook, consisting of cells that can be run independently to have access to partial results in a simple manner. The files produced natively by the program used for modeling (OptumG2), although they have the extension \(g2x\), they are, in reality, files that use the standard extensible markup language (XML), such that they are simple to manipulate using external tools. A \"\(g2x\)\" file is generated for each of the simulations that will be run using the Jupyter notebook and executed using the OptumG2 calculation engine, and the results are extracted from the model output file. Each of the files is generated automatically with upper and lower bound analyses and the desired input parameter values. Soil parameter values can be incorporated in the OptumG2 file by replacing their value directly with minor changes in the template file. However, the modification of the slope geometry, height, and inclination requires the modification of the geometry of the model. To this end, an initial slope formed by six nodes was used as a template geometry. The positions of nodes 1, 2, 5, and 6 are maintained in the different model executions, while the x and y coordinates of node 4 and only the y coordinate of node 3 vary. With this variation, the slope inclination and height required by each model generated using the Monte Carlo method are obtained. In Figure 3, a diagram of the model modification is shown. The workflow for model creation and calculation is divided into five stages. The first consists of importing the Python libraries necessary for the code to function, both to perform mathematical operations, read, and modify OptumG2 files. Next are the cells used to define the variables that will modify the geometry (height and inclination angle) and soil strength parameters (cohesion, friction angle, and specific weight), the IDs of the nodes on which the slope geometry depends, and the ID of the material of which the slope is composed. The system allows the target intervals for each parameter to be defined and generates random data using a uniform distribution of each parameter. In this phase, a list for each input and the number of elements equal to the number of simulations to be run are obtained. The third stage consists of the modification of the template and the generation of files for calculation. The soil strength parameters and specific weight values are assigned based on the material ID. The process of modifying the geometry and behavior model parameters is carried out iteratively, with a number of cycles equal to the number of simulations (n).