A multi-scale roughness rock joint model considering laboratory-scale irregularities using wear theories

The shear strength of a rock fracture is influenced by surface irregularities, geometric parameters, loading conditions, and rock mechanical properties. A new shear model, derived from the energy balance equation, explicitly accounts for the contributions of shear-off component, related to the indentation of surface roughness, and the contributions of basic friction angle and asperity sliding, related to the inclined friction component, to the total shear strength. The progressive roughness degradation is considered in the model by incorporating adhesion and abrasion wear theories. Additionally, multi-scale surface roughness is integrated in the model, as various scaled asperities have different influences on shear behaviour. Due to the distinct influences of various scaled asperities on shear behaviour, their contributions during shear are also taken into account within the model utilising multi-scale roughness theory. Moreover, the model has been implemented into three-dimensional distinct element code (3DEC) using the built-in programming language FISH and verified with experimental data incorporating laboratory-scale rock fractures. The proposed model offers new insights into roughness degradation and yields good prediction performance, as demonstrated by an average error (σ‾ave) of 4.95 % ± 0.03 for the τ−us behaviour, a Normalised Objective Function (NOF) of 0.16 for the us−un behaviour.