Toppling susceptibility of a single rock block resting on a regularly rough base

Toppling of individual rock blocks resting on an inclined surface has often been observed in nature. This instability mechanism has typically been analysed for simple block geometries, considering the contact between the block and the base where it lies is a planar surface. In this study, the authors analyse the case where this contact is a regularly rough surface. To do that, the authors resort to analytical limit equilibrium formulations, laboratory physical models and discrete element methods. All these approaches show a consistent trend of behaviour, where roughness does affect the toppling response. Regularly rough surfaces are studied in detail and a general analytical formulation able to show the potential influence of roughness on the block toppling response is derived. Additionally, some considerations are provided regarding the combined effects of rough bases and rounded corners on toppling stability. The authors show how under particular circumstances, roughness can control the potential failure mechanism of a block to produce toppling instead of sliding, and they eventually discuss the impact of rough bases on the toppling response of natural rock blocks. •The stability against toppling of a rock block resting on a rough surface is analysed.•Analytical, numerical simulations and physical models are applied.•All methods provide similar responses, which make the study reliable.•A general formulation to analyse toppling of a block on a regular rough surface is provided.