# Physical Vulnerability and Landslide Risk Assessment in Tegucigalpa City, Honduras
## 2 Materials and Methods
### Spatial Probability  
A physical model was applied to characterize the spatial probability (Pt). For this purpose, the PISA-m program was utilized [31]. This program integrates a physical model based on the infinite slope and treats the uncertainty of input parameters using the first-order second-moment method (FOSM). This method estimates the probability that the safety factor (_SF_) is less than 1 in each pixel. The equation used for the infinite slope is as follows [31]:  
\[SF=\frac{c_{r}\,+c_{s}\,+[q_{t}\,+Y_{m}D+(Y_{sat}-Y_{w}-Y_{m})H_{w}D\ ]cos^{2}\beta\ \tan}{[q_{t}\,+Y_{m}D+(Y_{sat}-Y_{m})H_{w}D]\sin \beta\ \cos\beta} \tag{4}\]  
where _SF_ is the safety factor; \(c_{r}\) is the cohesive strength of tree roots (strength/area); \(c_{s}\) is the cohesive strength of the soil (strength/area); \(q_{t}\) is the uniform load due to the weight of vegetation (strength/area); \(\Upsilon_{m}\) is the unit weight of wet soil (weight/volume): \(\Upsilon_{sat}\) is the unit weight of saturated soil below the water table (weight/volume); \(\Upsilon_{w}\) is the unit weight of water; \(D\) is the thickness of the soil above the breaking surface normalized by the thickness of the soil height of the water table above the breaking surface normalized by the thickness of the soil (dimensionless); \(\beta\) is the slope (degrees); and \(\mathcal{O}\) is the internal friction angle (degrees).  
In order to use the PISA-m program, three raster coverages were created, all having the same extension and pixel size. These included (i) Digital Elevation Model (DEM) coverage; (ii) \"soil\" coverage, containing the colluvium and residual soil layer; and (iii) \"trees\" coverage, showing the different types of vegetation cover in the study area. The tree resistance properties were considered to be zero, as there is no significant tree coverage in the study area. The DEM was created with contour intervals of 10 m and a pixel size of 10 \(\times\) 10 m. The contour data were provided by the municipality of Tegucigalpa and covers the entire study area. The layer of colluvium and residual soil was produced through geomorphological mapping, involving the classification of landforms via photo interpretation of aerial photos at a 1:10,000 scale, topographic analysis, and fieldwork [17]. In regard to those coverages, there were no missing data.  
In addition, a parameter file was generated for each type of colluvium and residual soil. These geotechnical parameters were determined using average values of local laboratory  
Figure 3: Colluvium and residual soil map.  
tests collected in the study area for each type of soil. It was assumed that these parameters followed a normal distribution, which is one of the requirements for applying the FOSM method [32]. The value of \(\mathrm{H_{w}}\) was assumed to be 1, indicating the most unfavorable condition, where the ground is completely saturated.  
In a previous publication [33], the infinite slope model has been used to characterize the SF in the study area. The results indicated that the model tends to underestimate landslide areas in low-slope terrains. Therefore, a review of the modeling results was carried out using expert criteria, in order to manually include potential landslide zones that were classified as stable by the model. The applied methodology was geomorphological mapping to classify certain landforms as landslides by means of expert criteria, combining aerial photo interpretation, topographic maps, and field observations.