The Influence of Roughness on the UCS of Discontinuous Jointed Rocks

Joint roughness and size effect are key factors controlling the uniaxial compressive strength (UCS) of discontinuous jointed rock masses. However, there is currently a lack of a unified quantitative model that can simultaneously characterize the roughness enhancement effect and the size weakening effect. Based on a two-dimensional numerical simulation, this paper constructs a discontinuous jointed rock mass model with different joint roughness coefficients (JRC = 2–10) and different rock sizes (100–300 mm). It systematically analyzes the stress–strain response, peak strength evolution, and strength fluctuation characteristics of the rock and establishes a relevant fitting relationship for UCS. The results indicate that UCS exhibits a significant exponential increase trend with the increase of JRC, while it shows a notable power function weakening trend with the increase of size. The strength fluctuation coefficient reveals the synergistic effect of roughness and size on the dispersion of strength and determines the characteristic size range for UCS convergence. The main innovations of this paper lie in (1) proposing an exponential enhancement model for UCS–JRC, (2) establishing a unified coupled prediction formula for the evolution of strength parameters with size, and (3) introducing the strength fluctuation coefficient and derivative criterion to achieve quantitative identification of characteristic dimensions. This study provides a new theoretical basis for predicting the strength of complex jointed rock masses and evaluating the scale effect in engineering.