A geometric terrain roughness model for rockfall simulation in a hard-contact framework

Rockfall simulations are highly sensitive to digital elevation model (DEM) resolution, because coarse terrain representations smooth micro-topographic roughness and may overestimate velocities, jump heights, and runout. This study presents a geometric roughness model that reduces this dependence while separating macroscopic topography from unresolved terrain roughness. The model is developed within a rigid-body nonsmooth dynamics framework. Roughness is introduced through explicit mathematical functions within terrain contact detection rather than being embedded directly in the DEM. It modifies both the terrain elevation used for contact detection and the local contact-frame orientation. Since roughness is evaluated only where required, the approach remains computationally scalable with respect to domain size and roughness resolution. In 2D, roughness is represented by sinusoidal functions with spatially varying amplitude and frequency. In 3D, spatially variable Perlin noise generates roughness fields that can be parameterised from commonly used roughness indices or representative grain sizes. The model is validated on the Chant Sura test slope using a centimetre-scale DEM as benchmark and coarser DEMs from 0.5 to 20 m, with and without added roughness. The proposed formulation substantially reduces the dependence of deposition patterns and velocity fields on DEM resolution. For high-resolution DEMs that already partially contain roughness, only roughness scales smaller than the DEM resolution should be added. At very coarse resolutions, deviations may still occur due to the smoothing of macroscopic terrain features. The formulation is computationally efficient, transferable to other rockfall frameworks, and treats roughness as a geometric property that can be combined with independent ground-interaction models.