Towards a stress-based stability criterion for rock slopes from 3D stress modeling of entire mountain massifs

Steep mountain landscapes are subject to gravitational stresses generated by elastic compression of the rock mass under its own topographic load, commonly referred to as dead-load stresses. This load induces shear stresses that promote rock failure. In turn, dead-load stresses also contain normal stresses acting perpendicular to internal rock surfaces, which increase frictional resistance and thereby contribute to the overall mechanical stability of the rock mass. However, the stresses are distributed unevenly because topographic load varies strongly with relief. Predicting the stresses from topography and rock properties is not trivial, which makes the prediction of failure difficult.

Despite this mechanical link, the role of the full three-dimensional stress state within mountain massifs remains difficult to quantify and is rarely incorporated into slope-stability concepts. In previous work, we used high-resolution three-dimensional linear elastic stress simulations to examine how stress fields reorganize during progressive topographic decay. Building on this approach, we explore the potential of stress-based stability metrics derived from full three-dimensional stress tensors to assess rock-slope stability across entire mountain massifs.

We compute the stress field beneath digital elevation models using the Finite Cell Method, a fictitious-domain approach that enables efficient and accurate linear elastic stress calculations for complex alpine topographies without the need for boundary-fitted meshes. This framework allows simulations at the scale of whole mountain ranges while retaining detailed resolution of near-surface stress variations. Based on the resulting stress fields, we introduce a simple Mohr-Coulomb-based formulation to estimate the minimum rock-mass cohesion required for stability under the local stress state, assuming a prescribed internal friction angle. This metric provides a spatially explicit measure of how close different parts of the landscape are to plausible rock-strength limits.

Our analysis focuses on spatial patterns of stress-limited stability and their relation to relief and slope geometry in steep alpine terrain. We examine how the estimated minimum cohesion varies across the landscape and whether regions of elevated cohesion demand coincide with known landslide source areas or zones identified as unstable by independent landslide models. The results demonstrate how three-dimensional stress information can complement purely geometric descriptors of slope stability and provide a physically motivated basis for evaluating rock-slope stability at the scale of mountain massifs.