**4. Results**

#### *4.1. Implementation of RES for the Estimation of Weighted Coefficients*

In this section, the results of the application of the RES method in the Attica Region are presented, such as the interactions among the selected parameters, the calculation of their weighting coefficients and finally the instability index accompanying with charts and tables which they decode and translate the geodata. As it was previously presented, the interaction matrix shown in Table 3 was coded using the Expert Semi-Quantitative method. For example, regarding the effect of lithology (P4) on rainfall (P6), it can be stated that there is no influence at all (coding: 0), whereas rainfall does affect lithology through the infiltrating and weathering-erosion process that may alter not only the mineralogical composition of a specific rock or soil of the slope but also influence their hydrogeological behavior too (coding: 2).

Note that, in Table 3, the sum of cause-and-effect (C + E) value for each parameter represents the "interaction intensity" term, which means how active that parameter is within the matrix system (i.e., the slope stability). On the contrary, the (C − E) value represents how dominant the variable is within the system: positive values of (C − E) represent a dominant variable, whereas negative values of (C − E) represent that the system is affecting the variable more than the variable is affecting the system [7]. More specifically, from Table 3 and Figure 7, it can be seen that the hydrogeological conditions are the most interactive parameter (C + E = 39) [e.g., has the greatest value (concerning C + E)], meaning those conditions play the most decisive role for landslide activation, whereas elevation is the least interactive (C + E = 18). This suggests that elevation does not depend on the influence of the other parameters, but it is an independent agent.

**Table 3.** Coding values for the interaction matrix of Attica Region.

**Figure 7.** Histogram of interaction intensity.

From the RES model and by focusing on the weights assigned to each parameter, it can be clearly reported that hydrogeological conditions contribute the most to landslide occurrence out of all the factors, followed by distance from streams, lithology, slope angle, rainfall, distance from roads, land use, distance to fault lines, aspect and elevation.

In Figure 8, the form of C vs. E constellation in relation to C = E line, defines the number of parameters that will be needed for calculating the instability index. So, according to the interaction intensity–dominance diagram (Figure 6b), the form of the C vs. E constellation is (almost) perpendicular to the C = E line, which means that (based on the aforementioned RES analysis) there is little range in parameter interaction intensity. On the contrary, there is a wide range in dominance (C − E values), so all the selected parameters will be required for the calculation of the instability index for each examined slope.

**Figure 8.** Cause–Effect diagram.

Supplementary, the following Table 4, decode and "translate" simultaneously the geodata acquired from our research and contribute in giving the necessary objective answer to the prognosis of the potential instability of the examined slopes of Attica Region. This can be accomplished by the estimation of the instability index, as clearly explained in Section 3.2.1.

A characteristic sample, 10 out of 220 cases of the computation results regarding the instability index, is given in Table 4. In this table, each examined slope (is depicted in the column "Slopes") is ranked according to Table 1 rating, taking into account in parallel the specific geological conditions that characterize it according to either the ad-hoc technical report we collected or field study we carried out. Afterward, for each slope site, every ranking of each parameter (each parameter is depicted in the second line under the title "Parameters", named as 1, 2, 3, ... , 10) is multiplied by its weighted coefficient (last line of the Table) respectively and each outcome, based on Equation (1) is added in order to yield the instability index for each slope. For example, the instability index of Slope (1) is estimated as follows:

Σ [Parameter (1): 4 \* 2.39 + Parameter (2): 1 \* 2.77 + . . . + Parameter (10): 2 \* 1.72] = 71 (3)

> In Table 5, the classification for relative landslide susceptibility is listed as proposed by Brabb et al. (1972) [50].


**Table 4.** Calculation of Instability Index based on Rock Engineering System methodology for a characteristic sample of 10 slope failures out of 220 ones in Attica Region.

> **Table 5.** Classification for relative landslide susceptibility proposed by Brabb et al. (1972) [50].


As it is shown in this table, the generated instability index that is greater than 53%, corresponds to extremely high relative susceptibility up to slope failure and that this is the crucial point for a planner or a researcher for producing a landslide susceptibility map for a particular examined area. This remark is going to be used extensively in the following sessions of this study.

#### *4.2. Correlation of Spatial Distribution of Slope Failures with the Predisposing Factors Using Statistical Analysis*

Based on the information of Table 4, and according to the ranking of parameters of Table 2, the following useful findings come out during the generation of the susceptibility map of the Attica region. Based on this analysis, it can be concluded that 211 out of 220 (96%) slope failures are in a distance from roads up to 50 m.

Concerning the aspect parameter, 37% of the examined slopes are primarily more abundant on Southeast-facing and secondly on Northwest-facing (34%). Based on the rating assigned to each geological formation (e.g., lithology), the highest (40%) one is observed at flysch (and debris) and secondly to carbonate rocks (37%). This remark was expected since the former ones are the most statistically frequent formations prone to landslides in Greek territory, whereas the latter ones are associated mainly with rockfall incidents in many parts of Greece.

Regarding hydrogeological conditions, carbonate rocks with medium to high permeability due to karstification and secondary fragmentation correspond to the highest (35%) category of permeable rocks in this study. Based on the comparison among rainfall data and landslide occurrences, it was established that landslides are more likely to take place

when the mean annual rainfall is between 400–800 mm. As far as land use parameter is concerned, landslides reported mostly in urban areas (62%) while based on the results given for the elevation, it was found that the landslides develop preferentially on 0–200 m of altitude (63%).

Furthermore, a large portion of landslides (58%) are located near to the hydrographic network in relation especially to the undermining of the banks between 0 m and 50 m. Such places were recorded in many streams (mostly) in the Athens basin (such as those of Kifisos river, Chelidonous, Sapfous, Penteli, Eschatia stream).

Summarizing, the percentages of landslides per each class of predisposing factor are illustrated in the following Figure 9.

**Figure 9.** *Cont*.

**Figure 9.** Percentage of landslides in each class of the causal and triggering factor of landslide occurrence.

#### *4.3. Landslide Susceptibility Map*

The subdivision of the predisposing parameters into subclasses (from Table 2) was used for the evaluation of the final slope failure susceptibility map. This map was generated in a GIS environment, through the use of different layers-thematic maps (Figure 10a–j). The data used for the preparation of these layers were obtained from different geodata sources among which are the Digital Elevation Model from Hellenic Cadastre S.A. and a mosaic geological map from the Hellenic Survey of Geological and Mineral Exploration. All data layers were digitized either from the original thematic maps or derived from spatial GIS calculations and finally were converted into grids with a cell size of 20 × 20 m. Afterward, weights and rank values to the reclassified raster layers (representing predisposing factors) and to the classes of each layer were assigned, respectively. This was realized with the use of the previously extended analyzed methodology of RES. Finally, the weighted raster thematic maps with the assigned ranking values for their classes were multiplied by the corresponding weights and added up (through the ArcGIS tool of the weighted sum) to yield the slope failure map where each cell has a certain landslide susceptibility index value. The reclassification of this map represents the final susceptibility map of the study area, divided into susceptibility zones according to Brabb et al. (1972) [50] classification (Figure 11). The landslide susceptibility index (LSI) values in the final susceptibility map were classified into five categories, namely "Low-Middle", with Instability index (Ii) < 25, "High" with 25 < Ii < 42, "Very High" with 42 < Ii < 53, "Extremely high" with 53 < Ii < 70", and "Landslide" with Ii > 70%. From this classification, it can be clearly notified that the higher the LSI, the more susceptible the area is to landslides (instability index higher than 70%).

**Figure 10.** *Cont*.

**Figure 10.** *Cont*.

**Figure 10.** Thematic raster maps of the ten (10) landslide parameters used for the estimation of Attica region susceptibility: (**a**) Distance from roads, (**b**) Slope, (**c**) Aspect, (**d**) Reclassified geological map, (**e**) Hydrogeological conditions, (**f**) Rainfall, (**g**) Land use, (**h**) Distance from streams, (**i**) Distance from tectonic elements, (**j**) Elevation.

> From Figure 11, some further findings that come out are as follows (Table 6, Figure 12):


**Table 6.** Correlation between instability index and susceptibility coverage class in km2.

From the above pie diagram, it is clear that 43.09% (39.85% + 3.24%) of the examined area is associated with an instability index greater than 53%. Furthermore, it can be added that 122 km<sup>2</sup> (3.24%) of the total examined area are correlated to potential landslide occurrence. Public authorities responsible for auditing and supervising technical works should be aware of these findings, so as to take the appropriate advance, mitigation measures against the possible initiation of potential disastrous landslide phenomena taken place in these proposed, for slope failures, areas.

**Figure 11.** The Susceptibility map of Attica Region.

**Figure 12.** Pie diagram depicting the landslide susceptibility coverage class in km<sup>2</sup> for Attica region.

#### *4.4. Validation of the Landslide Susceptibility Map*

For having scientific significance in any generated model, the most important component in prediction modelling, is to implement a validation of the prediction results [51]. Thus, in the final landslide susceptibility map, we compared the results with the distribution of the 220 slope failure events that had occurred in the examined area. The predicted map showed very satisfactory results and particularly, at the susceptibility map of the Attica region, 68% of the locations of actual and potential landslides correspond to the "Extremely high" and 21% are associated with a landslide (Figure 13, Table 7).

**Figure 13.** Correlation among number of examined slope failures, instability index, and susceptibility classification. Blue color corresponds to the number of slope failures, orange color is linked with instability index percentage associated with susceptibility categories.


**Table 7.** Correlation among number of examined slope failures, instability index, and susceptibility classification.

Moreover, another method for validating the above mentioned, was the implementation of the confusion matrix. It is a table that is often used to describe the performance of a classification model on a set of test data for which the true values are known [52]. We used the confusion matrix for a binary classifier e.g., ( α) the existence of landslides with instability index greater than 53% and (b) the no existence of landslides (with instability index less than 53%). Each row of the matrix represents the instances in an actual class while each column represents the instances in a predicted class (or vice versa). In our case, In Table 8, four different combinations of predicted and actual values were used.

**Table 8.** Confusion matrix of the landslide susceptibility map validation.


Where: TN means when the examined slope does not correspond to landslide, how often does it predict no, FP means when the examined slope does not correspond to landslide, how often does it predict yes, FN means the falsely predicted landslide, TP means when the examined slope correspond to landslide, how often does it predict yes.

The following is a list of rates that were computed from the confusion matrix for a binary classifier:

• Accuracy: Overall, how often is the classifier correct?

$$(\text{TP} + \text{TN})/\text{total} = (174 + 3)/220 = 0.80\tag{4}$$

• Precision: Out of all the positive classes we predicted correctly, how many are actually positive.

$$\text{TP/predicted yes} = 174/195 = 0.89\tag{5}$$

• Prevalence: How often does the yes condition actually occur in our sample?

$$\text{actual yes/total} = 196/220 = 0.89\tag{6}$$

From the above, analytically presented, it is clear that the described RES methodology has 89% precision.

In addition, the validation of the generated susceptibility map was tested with two additional landslide databases. These are (a) the 98 polygons derived from Oregon methodology as previously mentioned, and (b) erosion lines derived from a project delivered by the Hellenic Survey of Geological and Mineral Exploration concerning the Mandra area flooding susceptibility [53]. Particularly, it was found that regarding the Oregon protocol, in the generated landslide susceptibility map of the Attica region, 49% of the

defined polygons correspond to the "Extremely high" category and 33% are associated with landslides. Concerning the rest of the delineated areas, it is proposed to conduct geological–geotechnical investigations to define the potential of the slopes to failure.

Finally, the erosion lines which were defined by the aforementioned research institute were in accordance with the instability index greater than 70%.

Practical use of the final susceptibility map is the implementation it may have during the planning, design and construction of various important infrastructure projects. Even though it is not advisable to be used for local or site-specific planning, C.J. Van Westen (2016) [54], recommends the following use of the above-mentioned susceptibility classes.

## **Low susceptibility zones**

In those areas, with respect to planning and constructing civil engineering projects, no special care should be taken by planners and engineers.
