*4.2. Numerical Approach*

Six simulations were carried out for each section: three using the conditions described above (min, mean and max) and three including the presence of a shallow water table (as often evidenced during field surveys).

The results of the simulations are shown in Figures 8 and 9 and Table 2. More specifically, Figures 8 and 9 show the plots of the simulations that evidenced the lowest FoS values (i.e., worse geotechnical parameters and presence of groundwater); Table 2 includes all the FoS values obtained from the simulations and any correspondences with what was observed in the field (geomorphological model). The same table also reports the failure models used by the software for any simulation.

**Figure 8.** Results of numerical simulation (Sections 1V, 2V, 3V, 4V, 5V). From left to right: geotechnical cross-section, mesh and model result. 1—slope and colluvial deposits; 2—arenaceous-conglomeratic bedrock; 3—arenaceous-pelitic and pelitic-arenaceous bedrock; 4—mainly clayey bedrock; 5—mainly pelitic-arenaceous bedrock; 6—mainly arenaceous-pelitic bedrock; 7—weak layer/ductile deformation zone; 8—water table.

**Figure 9.** Results of numerical simulation (Sections 6V, 1M, 2M, 3M, 4M). From left to right: geotechnical cross-section, mesh and model result. 1—slope and colluvial deposits; 2—arenaceous-conglomeratic bedrock; 3—arenaceous-pelitic and pelitic-arenaceous bedrock; 4—mainly clayey bedrock; 5—mainly pelitic-arenaceous bedrock; 6—mainly arenaceous-pelitic bedrock; 7—weak layer/ductile deformation zone; 8—water table.


**Table 2.** Factor of safety resulting from the numerical modeling and correspondence with field evidence.

> Sections 1V, 2V and 3V (Figure 8) show high stability in all lithological conditions, with or without the presence of a water table, with FoS values ranging between 3.06 and 8.47 (Table 2).

> Nevertheless, the obtained values of FoS as well as shape and depth of the failure surfaces, as evidenced by the model results, are unrealistic and clearly conditioned by the assumed boundary conditions; therefore, for these specific sections, we can only hypothesize a high stability condition and a perfect congruence with the results of the field surveys, which did not show any appreciable phenomenon.

> Section 4V (Figure 8) shows a clear instability only in the presence of groundwater, when the FoS drops below 1; in dry conditions the FoS ranges between 1.28 and 1.50, resulting in a condition of moderate stability. The failure surface is located very close to the surface, within the debris cover, while the bedrock, even when dip-sloping, remains almost stable in all conditions. In this case, the model reflects quite faithfully the reality, as a shallow mudflow was observed within a secondary valley filled by colluvial deposits.

> Models relating to the section 5V (Figure 8 and Table 2) evidenced highly unstable conditions (FoS between 0.97 and 1.17) only in the presence of water and in dry conditions. As with the previous model, the failure surface is located in the upper portion of the deposits, near the contact with the arenaceous-conglomeratic body of Mount Falcone; the presence of weak levels and ductile deformation zones, as previously described, does not seem to influence the FoS. Unlike the previous case, however, the geomorphological model only partially reflects the numerical one. The field surveys showed the presence of a complex gravitational movement compatible with a slide (probably rotational) in the upper portion of the slope and with a flow in the medium–low portion. The presence of water within the colluvial deposits, observed mainly in autumn and spring, originates at the contact between the overlying arenaceous-conglomeratic body acting as an aquifer and the underlying low-permeability pelitic-arenaceous formation.

> Section 6V (Figure 9) shows high instability in all conditions, with and without the presence of water, with FoS between 0.71 and 1.13. Although the stratigraphic setting of the clayey bedrock is favorable to the occurrence of gravitational movements, the failure surface is localized in the medium–low portion of the slope, at the contact between the bedrock itself and the colluvial deposits above. These simulations, however, do not find correspondence in the geomorphological model: any significant phenomenon was observed in the field.

This could be linked to an incorrect assessment of the real thicknesses of the deposits, the latter having been estimated in this sector without the aid of geognostic surveys.

The simulations carried out with regard to sections 1M and 2M (Figure 9) yielded similar results, with evidence of instability in the presence of water (FoS between 0.89 and 1.16) and moderate stability in dry conditions (FoS between 1.22 and 1.51). The shear-strain belts are located in positions similar to the previous case, in the middle portion of the slope and inside the colluvial deposits. In these two simulations, the setting of bedrock (i.e., the presence of the weak levels within the pelitic-arenaceous formation in section 2M) does not seem to affect the stability of the slope. The correspondence with the field evidence is different: none in section 1M and good correspondence in section 2M. Taking into account previously mentioned factors, the reason, in the first case, could be found in an incorrect evaluation of the overall thickness of continental deposits.

Finally, sections 3M and 4M (Figure 9) also provided similar results, this time in favor of stability, with the FoS always higher than 1.30 (max = 1.85): The presence of a favorable stratigraphic setting (sub-horizontal or slightly counter dip-slope strata), lower slope angle and limited thickness of colluvial deposits certainly affected the result of the simulations. However, a fair correspondence with the field data was found only in section 3M; in the case of section 4M, on the contrary, a fairly evident mudflow was observed inside the valley, E–W oriented, which originates from the arenaceous-conglomeratic body of Mount Falcone.

By analyzing all the simulations, it is possible to form some general considerations:


#### **5. Discussion and Conclusions**

Numerical models and, in particular, finite difference programs represent a powerful resource for the study and analysis of gravitational phenomena. Specifically, software such as FLAC/Slope, having characteristic geotechnical parameters of soils and rocks, can be used to carry out important assessments on the stability of the slopes and provide an estimate of the FoS. These assessments can then be used successfully both for purposes related to civil engineering (construction of buildings and infrastructures, effectiveness of slope reinforcement works, etc.) and, more generally, for the assessment of landslide susceptibility of variously sized sectors of the slope. Although they provide numerical results that are indispensable for any type of design and planning, the limits of the models are closely linked to the availability and correctness of the input parameters, which are often missing and limited to single laboratory analyses or estimation through direct observations.

The geomorphological model, based on field observations of the processes active in an area, allows a broader and certainly more articulated evaluation of gravitational phenomena; nevertheless, since it consists of an exclusively qualitative analysis, it cannot provide indices and parameters for performing numerical calculations.

A combined approach that integrates the two models can certainly provide mutual advantages: the ability to confirm and quantify the phenomena observed in the field (the geomorphological model) and to verify and modify model parameters and geometry (the numerical model).

The combined approach, however, when compared to the standard methods (i.e., the statistical methods currently used in Italy for LHA), requires a greater effort both in

economic terms and in terms of human resources, since it is necessary to proceed with an update and, often, implementation of the field data. This is all the more onerous in the case of a similar methodology as a standard at the national level where there are large disparities (not only economic) between different regional realities. On the other hand, the possibility of having an updated product that is more functional for professional needs or for the planning of particularly critical areas cannot be separated from an approach that provides for a continuous synthesis between real data and numerical models.

The present study, through this type of approach, provides a more objective evaluation of the mechanisms governing landsliding in a typical geological–structural context, characterized by a monoclinal setting and the presence of lithotypes of different nature and consistency.

More specifically, it was possible to verify that:


The above considerations could provide further confirmation and perhaps be extended to different morphological–structural contexts, through new detailed surveys and a precise characterization of the buried or outcropping lithotypes.

In conclusion, the proposed approach, which can be defined as semi-quantitative, can be proposed as a valid alternative for LHA in all those countries where specific regulatory indications are absent. The obtained results evidence usefulness and limits of the methods currently used in Italy and, in particular, sugges<sup>t</sup> how a combined use of geomorphological surveys and numerical simulations, pending clearer and universally accepted regulatory indications on the methods to be used for the LHA, seems at the moment the most suitable choice both in economic and safety terms.

**Author Contributions:** Conceptualization, M.M. and M.B.; methodology, M.M.; software, M.M. and M.G.; validation, G.P., P.F. and D.A.; formal analysis, M.M.; investigation, M.M. and M.B.; resources, M.M. and M.B.; data curation, M.M. and M.B.; writing—original draft preparation, M.M. and M.B.; writing—review and editing, M.M. and M.B.; visualization, M.M., M.B. and G.P.; supervision, M.M., M.B. and G.P.; project administration, N/A; funding acquisition, N/A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
