An open-source code to calculate the spatial distributed roughness from 3D point clouds for rockfall simulation models

The Geomatics Engineering (EGEO) research group of the Universitat Politècnica de Catalunya (UPC-BarcelonaTech) has developed, a 3D lumped mass simulator of block trajectories, called RockGIS, which considers the fragmentation of blocks along its propagation. In this type of simulators, digital elevation models in raster format are usually used. This information allows considering the apparent angle of friction presented by the contact surface between the ground and the detached block from the cliff. One of the limitations of considering a lumped mass approach when simulating the failure of a block is that its relative position at impact with the slope is unknown, since the geometry is not explicitly accounted for. The rebound depends on the size of the impacting fragment. It is common to use different sets of restitution coefficients for different block sizes, but when considering fragmentation, the model must be able to reproduce this different behavior depending on the size of the block. The roughness of the terrain plays an important role in this effect. Therefore, it is convenient to have models of the spatial distributed roughness of the slope.

In these models the local roughness is not represented due to the lack of resolution. Rockfall propagation programs usually assign roughness values to different areas based on field measurements or consider global values of roughness, which are often unrealistic. This is most evident in the spread of blocks in scree deposits. These have a heterogeneous granulometric distribution, with the accumulation of fragments of small dimensions in the upper parts with low roughness (a highly deformable area with low coefficient of restitution), while the large blocks accumulated at the foot. The dense point clouds that can be provided by photogrammetry or laser scanning (terrestrial TLS or lately airborne in a UAV) allow us to better estimate the roughness of the surface. Focusing on this kind of higher resolution 3D point cloud, an algorithm to characterize the roughness of the terrain has been developed, based on a statistic of the heights of points respect a local reference plane, established by RANSAC method, and in a certain neighborhood. To reduce the computational time required, the surface has been divided into simpler tree data structures, called octree. Once the octree structure is done, a calculation of the roughness can be obtained from the 3D point cloud for each point and its nearest points within a distance r. Then, the values obtained on the 3D point cloud at the required level of scale, are projected to a raster grid in order to be read by the simulator of rockfall trajectories. This study has been developed in the framework of the Georisk project (Reference: PID2019-103974RB-I00, funded by MCIN/ AEI/ 10.13039/ 501100011033).