Three-dimensional rockfall modeling in GRASS GIS with r.stone

We present an open-source version of the software STONE [1] for the three-dimensional simulation of rockfall trajectories. The software implements a lumped mass kinematic model that simulates trajectories in a spatially distributed manner, in areas of up to thousands of square kilometers, starting from topographic (digital terrain model, DTM) and ancillary data easily manageable in GRASS GIS [2,3].

The rockfall phenomena that can be described with the STONE model are those involving the fall of individual blocks, which do not interact during their motion with other moving blocks/boulders, and whose trajectory can be described by a combination of parabola sections (free fall), bouncing on the ground and rolling.

In addition to a DTM, minimal data required for running the r.stone module are: a raster map of the numerical coefficient of friction, relevant for the rock rolling phase, two maps of numerical coefficients of normal and tangential restitution, which control the loss of kinetic energy at each bounce, and a raster map defining the initiation points of trajectories (sources). The latter is the most distinguishing input of the software, as the simulated motion of the falling block starts at these user-defined points of the topography.

In this contribution, in addition to presenting the new software, we discuss methods to obtain the location of rockfall sources on large areas, based on different strategies. These strategies mostly involve using maps of known source locations, either observed in the field or inferred from expert mapping, and generalizing them to other possible source locations with statistical and/or machine learning methods, under the common denominator of using information from a DTM as a starting point. In the definition of rockfall sources, specific triggering events can be taken into account, such as earthquakes [4,5] or intense rainfall events [6].

The main output of the model is the count of trajectories crossing each DTM grid cell, for given source locations and number of simulated trajectories. The output can be ascribed a probabilistic meaning, to obtain a physically-based susceptibility map for rockfalls. The absolute values in the raster output can be classified according to different criteria, mostly depending on the specific target relevant to the study, typically transport corridors (railways [3], roads [7,8]), buildings, and other urban infrastructure [9].

The software manual is available on the GRASS GIS addons repository [10].

[1] F. Guzzetti et al., Computers & Geosciences 28, 1079-1093. https://doi.org/10.1016/S0098-3004(02)00025-0

[2] F. Guzzetti et al., Environmental Management 34, 191–208. https://doi.org/10.1007/ s00267-003-0021-6

[3] M. Alvioli et al., Rockfall susceptibility and network–ranked susceptibility along the Italian railway. Engineering Geology 293, 106301. https://doi.org/10.1016/j.enggeo.2021.106301

[4] M. Alvioli et al., Landslides 21(1) 1-16 (2024). https://doi.org/10.1007/s10346-023-02127-2

[5] M. Alvioli et al., Geomorphology, 429, 108652 (2023). https://doi.org/10.1016/j.geomorph.2023.108652

[6] M. Alvioli & M. Melillo (in preparation)

[7] B. Pokharel et al., Bulletin of Engineering Geology and the Environment 82, 183. https://doi.org/10.1007/s10064-023-03174-8.

[8] M. Santangelo et al., Nat. Hazards Earth Syst. Sci. 19, 325-335 (2019). https://doi.org/10.5194/nhess-19-325-2019

[9] M. Santangelo et al., Journal of Maps 17, 124 (2021). https://doi.org/10.1080/17445647.2020.1746699

[10] https://grass.osgeo.org/grass-stable/manuals/addons/r.stone.html