## 4 Characterisation of the Fracture Network  
A dense network of fractures is an essential factor contributing to the detachment of rock fragments from the quarry walls within Bednarski Park. Particularly unfavourable are fractures whose surfaces are parallel or nearly parallel to the exposed rock faces, with spacing typically not exceeding several tens of centimetres. Often, the inclination of the rock wall corresponds closely to the dip of these parallel fractures. Such structural arrangements pose a significant risk of the relatively shallow sliding of individual rock blocks and deeper, structurally controlled slope failures.  
As part of the investigation, a detailed characterisation of the fracture network was conducted for each defined sector (Figure 2). The fractures were classified into distinct joint sets (A-E), and stereographic projections of these sets were generated (Figure 7--example projections for Sector 1). The field investigations and joint set classification were conducted based on the guidelines of the PN-EN ISO 14689 standard [51].  
Figure 5: Sector 5: (a) 3D view of the Sector 5 slope generated from a 0.25 m resolution LiDAR Digital Terrain Model (DTM) with a draped surface slope gradient. Transparent plates indicate faults. Other symbols are explained in the legend of Figure 2: (b) fragment of Sector 5. Fault surfaces (red transparent areas) (attitude parameters: 296/73—left fault and 298/85—right fault). The area between and to the right of the faults consists of fault breccia—levelling rod shown for scale (2 m length) (50\({}^{\circ}\)02\({}^{\prime}\)27.3\({}^{\prime\prime}\) N 19\({}^{\circ}\)56\({}^{\prime}\)57.6\({}^{\prime\prime}\) E).  
Figure 6: Sector 7: (a) 3D view of the Sector 7 slope generated from a 0.25 m resolution LiDAR Digital Terrain Model (DTM) with a draped surface slope gradient. Transparent plates mark the locations of faults. Other symbols are explained in the legend of Figure 2: (b) slope fragment of Sector 7. Red transparent area—fault with attitude parameters 284/88. The red contour line serves as a scale indicator (contour length 2 m) (50\({}^{\circ}\)02\({}^{\prime}\)29.5\({}^{\prime\prime}\) N 19\({}^{\circ}\)56\({}^{\prime}\)51.8\({}^{\prime\prime}\) E).  
To incorporate joint sets into the numerical analyses, the orientation parameters of each joint set (dip direction, dip angle, and spacing) were averaged, as determined through detailed mapping within each sector (Figure 7). The averaging process was applied to discontinuities that exhibited similar dip directions and dip angles to ensure representative values for modelling purposes. The summarised orientation parameters of the joint sets are presented in Table 1.  
Figure 7: Stereographic projections of the identified joint systems—Sector 1: (**a1–a4**) stereographic projection onto the lower hemisphere: (**b1–b4**) intersection points of normal to joint surfaces with the lower hemisphere (pole projection).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Sector** & **Joint** & **Mean Dip** & **Mean Dip** & **Mean Dip** & **Mean** & **Min/Max** & **Standard Deviation** & **Infill** \\  & **GROUP** & **Direction** & **Angle** & **Spacing [m]** & **Spacing [m]** & **Spacing [m]** & **of Spacing [m]** & **Infill** \\ \hline  & A1 & 306 & 81 & 0.76 & 0.10/3.00 & 0.744 & none \\ \cline{2-8}  & A2 & 115 & 80 & 12.16 & - & - & breccia \\ \cline{2-8}  & A3 & 140 & 76 & 12.92 & - & - & none \\ \cline{2-8}
1 & B1 & 30 & 79 & 0.47 & 0.24/0.81 & 0.200 & humus \\ \cline{2-8}  & B2 & 204 & 82 & 1.13 & 0.30/2.65 & 1.080 & humus \\ \hline \hline \end{tabular}
\end{table}
Table 1: Averaged orientation parameters of discontinuity sets for the designated sectors.