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1 2023

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A mathematical approach to calculating slope stability under physical triggering forces. Application to landscape mechanics

Khaber Larbi, Zighmi Karim, Hadji Riheb

Geomatics, Landmanagement and Landscape

2023

no. 4

97--112

In the field of land management, the limit equilibrium calculation method is a mathematical method that harmonizes the complex interplay of diverse factors determining the slope stability. Rooted in mechanical and mathematical principles, this method has paramount significance for guiding the course of safe land management in mountainous regions, especially in the case of infrastructure development projects. Conventional limit equilibrium techniques, while providing preliminary stability assessments, often neglect key factors that can trigger slope failure. These approaches traditionally ignore the spatial variations in soil properties, the temporal dynamics of phenomena, the kinetic responses to external loads, the complexities of geological formations, and the influences of the hydrological and climatic conditions on slope stability. Our innovative method adopts an enriched mathematical framework that redefines the landscape of force equilibrium techniques. We meticulously tailor this framework by adapting the foundational relationships derived from the Mohr-Coulomb shear strength criterion to accommodate the spatially variable geomechanical parameters. This adaptation allows us to capture the nuanced shifts in mechanical properties over the extent of the slope. Furthermore, we introduce supplementary equations that seamlessly integrate the influences of traffic-induced loads and hydraulic pressures, while also statistically quantifying the contributions of stabilizing structures. To determine the efficacy of this geomatic and landscape-centric numerical tool, we have subjected it to rigorous testing on a test slope. The outcomes derived from our mathematical model reveal the primacy of traffic-related forces as the main destabilizing agents, contrasted with the strengthening effects of reinforcements in maintaining slope stability.