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

An accurate prediction of the shear strength in rock discontinuities requires ac-counting for surface roughness, which is neglected in the classical Mohr–Coulomb theory. This study presents a fractal-enhanced modification of the criterion by directly incorporating the surface fractal dimension as a state-dependent parameter that governs cohesion and the internal friction angle. Fractal dimensions were reliably quantified using dual methods, box-counting and power spectral density, with strong agreement (R² = 0.98, mean deviation < 0.02), ensuring an objective and scale-invariant input. The results indicated that both the cohesion and friction angle increased nonlinearly with the fractal dimension, leading to a dynamically adjustable failure envelope. The modified model predicts up to 25–40% higher strength for rough joints than classical estimates, aligning closely with the experimental data. The criterion, constructed within the principal stress space and integrated into a fractional-order damage law, effectively characterizes the history-dependent failure process of the structure. The robustness of the solution was verified through Lyapunov stability analysis. The application of the Banach fixed-point theorem ensures the continuity and uniqueness of the solutions. Furthermore, the use of the fractal dimension to assess dynamic changes in fractality during shearing confirms that the fractal dimension is in a mechanical state. This fractal-based framework successfully linked microscale topography to macroscale strength, providing an intuitively grounded approach for the predictive stability assessment of geomechanics.