When Relief Becomes Unstable: Analyzing the Role of Tensile and Hybrid Fractures in Maximum Escarpment Heights

Slope stability description through mechanical laws has important implications for Earth morphology understanding and risk assessment. Previous research studies have shown that shear, tensile, and hybrid fractures can be observed experimentally and in the field, but their description by a single equation is still an open debate. Fracture envelopes able to contemporaneously describe these three fracture modes differ significantly from the Mohr–Coulomb law. Despite the need to apply such a law at all scales, from the laboratory to the mountain range, the fracture criterion that characterizes all types of fractures is rarely used in geotechnical engineering and geological investigations. In order to analyze the stability thresholds of large-scale relief, the current work examines the effects of considering the Griffith criterion with variable rock traction instead of the Mohr–Coulomb law using a modeling approach. The difference estimated for the maximum relief using these two different rupture criteria could be of the same order as those caused by geological phenomena, such as with or without seismic activity, or those caused by destabilization processes (tilting vs. landslide). When compared to the modified Griffith criterion, the Mohr–Coulomb law tends to overestimate the maximum escarpment height. The results are examined in relation to Carrara marble, which serves as a case study for the theoretical framework.