Computing the state of stress in mountain massifs undergoing topographic decay

Mountain relief results from a delicate balance between erosion by rivers and glaciers, which increases the relief and thus topographic stresses, and mass wasting processes, which counteract them. These processes involve complex interactions of mechanical failure, stress redistribution, and material transport, which collectively govern the evolution of alpine landscapes.  Understanding these interactions is crucial when it comes to assessing geological hazards but also to gain deeper insights into landscape evolution, especially for landscapes that are transitioning from a glacial to a fluvial state.   

This study uses an advanced computational framework to investigate how landslides influence the state of stress in mountain massifs undergoing topographic decay. We use a probabilistic landslide simulation model focused on material detachment (without tracking deposition), combined with the Finite Cell Method (FCM) for stress modeling, to analyze variations in the stress state of a mountain massif at successive topographic snapshots following rockfall events. The FCM enables precise, three-dimensional stress analyses across entire mountain ranges by leveraging the flexibility of fictitious domain approaches. Traditional methods, such as finite element techniques, rely on boundary-conforming meshes tailored to complex topography. These meshes are computationally intensive to generate and refine, especially for large-scale models. In contrast, the FCM operates on simpler, regular grids, enabling scalable and efficient analysis of large and complex terrains. Its adaptive integration schemes ensure high accuracy without the need for computationally expensive mesh refinement tailored to irregular geometries. 

We applied this novel approach to mountain massifs located at the three Austrian UNESCO Global Geoparks featuring iconic alpine landscapes characterized by steep slopes and active landslide processes. Our results show significant reductions in peak shear stresses following rockfall events, with stress maxima strongly correlating to steep valley flanks, highlighting areas of potential failure. Stress redistribution following landslides reduces localized stress concentrations, leading to a more homogeneous stress state and resulting in stabilization of the remaining rock mass. This finding supports the hypothesis that mass-wasting processes regulate topographic relief by limiting hillslope steepness. In contrast to traditional topographic metrics, which focus solely on surface features, our framework enables the determination of subsurface stresses and gradients, providing valuable insights into slope failure mechanics. This is critical for advancing predictive models of geological hazards and enhancing landscape stability assessments. By incorporating three-dimensional stress analysis, this framework offers novel insights into landscape evolution and a more refined understanding of the equilibrium between relief-forming and relief-reducing processes.