Real-time slope stability quantification: Emergent framework coupling landslide displacement with damage mechanics and renormalization group theory

Empirical observations have revealed the dynamic evolution of slope stability with landslide displacement, yet existing methods lack a rigorous mechanical framework to characterize this time-dependent process. To address the theoretical limitations of conventional early warning systems that depend on kinematic parameters (e.g., velocity and acceleration), this study develops a multiscale modeling framework integrating damage mechanics and renormalization group theory. We propose a shear constitutive model incorporating progressive rock damage and establish critical state criteria through renormalization group theory, deriving a displacement-coupled dynamic safety factor equation. Validation via field data from a slope engineering project and the finite difference method (FDM) simulations demonstrates two critical advancements: (1) The non-uniformity of overburden normal stress across the slip surface leads to spatially varying shear constitutive curves in different regions; (2) Slope stability displays nonlinear evolutionary phases (elastic–plastic transition → accelerated degradation → residual state) directly linked to displacement progression. This framework pioneers a physics-based mapping between displacement monitoring and slope stability states, establishing mechanistic foundations for intelligent early landslide warning systems.