## 4 Hazard Analysis Methods
### Determination of Basic Hazards  
For the basic hazard zoning, the safety factor was determined for each work unit, which was defined by the mesh and the soil columns obtained. The calculation of the safety factor was based on the infinite slope method in each of the work cells. The safety factor equation, in this case, is expressed as follows (2010):  
\[F.S.=\frac{C^{\prime}b\text{sec}(\upalpha)+\left[\gamma bh\text{cos}(\upalpha)- \gamma_{w}h_{w}b\text{cos}^{2}(\upalpha)-k\gamma bh\text{sin}\upalpha\right] \text{tan}(\upbeta^{\prime})}{\gamma bh\text{sin}(\upalpha)+K\gamma bh\text{cos }(\upalpha)} \tag{1}\]  
\(C^{\prime}\) and \(\upbeta^{\prime}\) are the strength parameters of the soil at the base of the soil column in terms of effective stresses.  
\(\upgamma\) is the unit weight of the soil.  
\(b\) is the width of the voussoir (cell width).  
\(h\) is the height of the ground above the potential slip surface.  
\(\gamma_{w}\) is the unit weight of water.  
\(h_{w}\) is the height of the water table, determined from the water table corresponding to a 20-year return period of rainfall.  
\(\upalpha\) is the angle of inclination of the failure surface.  
\(k\) is the horizontal acceleration coefficient for a return period of 100 years.  
The parameters \(C^{\prime}\) and \(\upbeta^{\prime}\) should be the values assigned in geotechnical studies for the defined geotechnical unit. The depth of the failure surface is taken as the depth of the soil or the depth of the contact between two units of different mechanical behaviors. The angle \(\upalpha\) can be assumed as the angle of the ground surface in the cell (Figure 7).  
Applying the equation, an analysis of random variables was carried out using the Monte Carlo method, which is a probabilistic model that can include an element of uncertainty or randomness in its prediction (2014). Testing 1000 simulations as an example to reduce the number of variables, it was decided to keep the slope parameter fixed, resulting in three models being carried out for three different slope values of the hillside. The aim was to analyze the behavior of the variation of parameters when there was a low, medium, and high slope, given that topographically, the hillside studied presents these three slope scenarios, and each one behaves in a different way. The results of these models yielded safety factors, which were tabulated and then plotted using a Gaussian bell (Figure 15) to observe the distribution of the data and the probability around a safety factor of less than 1.1. This is considered critical according to the SGC methodology for a scale of 1:5000 (Table 1) and is the warning criterion for the soil strength parameters and duration conditions reaching their limit due to the accumulated geotechnical deterioration for a specific slope and failure depth. The warning criteria were applied based on the \"screening\" of the different analysis scales where high threat levels were identified. When the safety factor falls below 1.1, an alert is generated. In this sense, it should be assumed that the resistant stress is decreasing in the face of a constant acting stress. In this way, the variation of parameters such as cohesion, friction angle, weight, and pore pressure determine how the resistant stress varies according to these parameters, which precisely define the concept of the AGD. RMR is a geomechanical classification used to characterize rock slopes.