A Fractal-Enhanced Mohr–Coulomb (FEMC) Model for Strength Prediction in Rough Rock Discontinuities

Accurate prediction of the shear strength of rock discontinuities requires accounting for surface roughness, which is a factor neglected in the classical Mohr–Coulomb criterion. This study proposes a fractal-enhanced Mohr–Coulomb model that incorporates the surface fractal dimension Ds as a geometric state variable governing both the cohesion and internal friction angle. The fractal dimension is treated as an objective, scale-invariant descriptor, computable via established methods, such as box-counting and power spectral density analysis, which are known to yield consistent results when applied to joint topography. The model predicts a nonlinear increase in shear strength with Ds, producing a dynamically adjustable failure envelope that can exceed the classical Mohr–Coulomb estimates by 25–40% for rough joints, which is consistent with trends observed in experimental shear tests. By linking strength parameters directly to measurable surface geometry, the framework provides a physically interpretable bridge between micro-scale roughness and macro-scale mechanical response. Although the current formulation assumes monotonic, dry, and quasi-static conditions, the explicit dependence on Ds offers a foundation for future extensions that incorporate anisotropy, damage evolution, and hydro-mechanical coupling.