# An Open-Source Algorithm for 3D ROck Slope Kinematic Analysis (ROKA)
## 3 Cases of Study  
### Case A: Northern Apennines--Calcareous Turbidites  
Case study A is represented by a 50 m length road cut, which is located along the upper Staffora Valley's right side in the Northern Apennines (44.733\({}^{\circ}\) latitude, 9.247\({}^{\circ}\) longitude). The slope is made up by Monte Antola flysch formation (Early Campanian-Early Maastrichtian) composed by dominantly turbiditic calcareous graded beds, calcareous sandstones, sandstones and maristones, with rare intervening thin, carbonate-free graded layers or uniformly fine-grained shale (Figure 5). Figure 5: The study rock slope located along the upper Staffora Valley. The area delimited by the dashed yellow line indicates the portion of the outcrop investigated by Terrestrial Digital Photogrammetry. The thickness of the more competent beds varies from a few centimeters to tens of meters, with an average thickness of 1.5 to 2 m. With an E-W direction and south-facing, the road cut is affected by frequent small rockfalls (in general \(\leq\)1 m\({}^{3}\)) that imperil the road SP-131. This outcrop was studied using the Terrestrial Digital Photogrammetry approach with a Canon EOS 5D 12.8 Megapixel camera (Canon Inc., Tokyo, Japan) from very close distances (\(\approx\)5 m). The 166 full-resolution pictures (with a mean resolution of \(\approx\)1.4 mm/pixel) were elaborated by the Metashape software (Agisoft LLC., St. Petersburg, Russia) [41], and a 3D point cloud representing the outcrop with 97 million points and a mean points density of 199,000 pts/m\({}^{2}\) was developed (Figure 6). The 3D model was georeferenced in local coordinates using Ground Control Points positioned onto an L-shape marker (Figure 7). The relative accuracy of the model was \(\pm\)0.5\({}^{\circ}\) in attitude and 0.1% in length. If we consider that the error of the traditional manual techniques of measure is 3-5\({}^{\circ}\) for the attitude [42], the obtained values can be regarded as fully acceptable [23; 43]. The discontinuities considered by the ROKA calculation were mapped manually onto the 3D point cloud through the CloudCompare software (with the methodology described in [23; 44; 45]. This methodology consists of selecting the points onto the 3D model representing the discontinuity traces and planes and then estimating the orientation of their best-fit plane. A total of 1919 discontinuities were detected (Figure 8). Figure 6: (**a**) Three-dimensional (3D) model representing the outcrop acquired using the Terrestrial Digital Photogrammetry and (**b**) a detail of the 3D model. The visible discontinuities, bedding and fractures, delimitate unstable rock blocks. The abbreviation NEE means NorthEast-East  
The features of the discontinuities detected onto the DOM (position, dimension and orientation) were exported into an XLSX file. Then, they were plotted onto a stereographic diagram to identify the main sets and perform the traditional KA. The analysis reveals the presence of five main sets (Figure 9): one related to bedding and the others related to fractures. After the analysis of the discontinuities orientation, the stereographic projection was used for the KA of the main modes of failure, planar failure, flexural toppling, wedge failure, and direct toppling (Figure 10). Figure 8: (**a**) The 3D discontinuities manually mapped onto the Digital Outcrop Model and (**b**) a detail showing the circular-shape considered for the discontinuities following the [PERSON]’s disc model [33]. Figure 7: (**a**) The L-shaped marker used to orient and scale the 3D model developed using the Terrestrial Digital Photogrammetry (TDP); (**b**) detail of the Ground Control Points (GCPs).