## 3 Methodology and Background Concepts  
With the scope to define and estimate the variation in the fracture abundance in the bedrock moving to major faults, fracture networks were characterized at sites located both along transects that are oriented normally to fault traces and scattered in their adjacent sectors. Sites were selected along the fault zones and in adjacent areas based on the extension and accessibility of bedrock outcrops (both natural or created by road cuts). At each site, fractures were collected using both linear scanline and areal sampling methods. In addition to the foliations, fractures observed in the field were qualified according to their dominant mode of wall rock movement, distinguishing joints (opening mode), faults (shearing modes), and veins (opening mode fractures with filling) (e.g., [25]). Figure 1: Regional geological settings of upper Susa valley (modified from Servizio Geologico d’Italia 1998 and 2020). Ellipses indicate investigated areas (1—Clavière-CesanaTorinese area; 2—Oulx sector; 3—Salbetrand area). Fracture collection along linear scanlines (ranging in length from 5 to 10 m on the basis of outcrop extension) was performed according to the International Society for Rock Mechanics and Rock Engineering (ISRM) suggestions (1978), and therefore, key attributes of individual fractures (i.e., type, orientation, persistence, spacing, and aperture) were defined. The orientations of sampled fractures were plotted in rosette diagrams to show the relative frequency of the fracture trends. Areal sampling method was applied to define spatial arrangement and topological relationships of fractures and to quantify the fracture abundance as fracture intensity P\({}_{21}\). In outcrops where scan lines were conducted, a representative portion of the general fracture state of the outcrop was photographed in a circular sampling area with a diameter of 1 m, using a reference cross. Pictures of each site were imported into QGIS software, the sampled fracture networks were digitized as lines (i.e., fracture traces intersecting or not), and then topologically qualified using the NetworkGT toolbox [39] (Figure 2). The network topological analysis is based on the fact that all the fractures, on the planar surface of analysis, represent isolated and/or interacting lines that are either terminating at their tips or cross-cutting or abutting other lines (Figure 2A). Therefore, a fracture (line) can consist of one or more branches bounded by isolated nodes (I-nodes), where the fracture is not geometrically connected to another fracture, and/or by connecting nodes (C-nodes), where the fracture cross-cuts other fractures (X-type nodes) or abuts to another with Y- or T-geometry (Y-type nodes). Then, the fracture network may include I-I (isolated) branches bounded by I end nodes, I-C (partly connected) branches bounded by I and X or Y end nodes, and C-C (doubly connected) branches bounded by Y and/or X end nodes (Figure 2B). The proportion of different node and branch types can be plotted onto triangular diagrams to characterize the fracture network [40]. Networks that are positioned towards the I-I corner of the triangle have a high percentage of isolated branches and, therefore, a low level of connectivity, whereas networks positioned towards the C-C corner of the triangle have a high percentage of interconnected branches. The connectivity can be expressed by the number of connections per branch (Cb), calculated using the following equation (Equation (1)):  
\[\mathrm{Cb}=(3\mathrm{N}_{\mathrm{y}}+4\mathrm{N}_{\mathrm{x}})/\mathrm{N}_{ \mathrm{b}} \tag{1}\]  
where N\({}_{\mathrm{x}}\) and N\({}_{\mathrm{y}}\) are the number of the X- and Y-nodes, and Nb is the total number of branches [40]. Cb is dimensionless in the range of 0-2. Fracture intensity is defined as the number of fractures per unit of sample length (P\({}_{10}\)), fracture length per unit of surface area (P\({}_{21}\)), or area of fractures per unit of rock volume (P\({}_{32}\)).