Joints can significantly affect the mechanical behaviour of rock masses. The presence of a joint set is crucial to the initiation and propagation of caving. A numerical approach to cave assessment requires a realistic joint constitutive model, and therefore produces better prediction of the cavability of the orebody. An asperity degradation model for rock joints has been developed that considers the progressive abrasion of a true roughness area over joint sliding. The magnitude of dilatancy is predicted to be decreased exponentially with the increase in shear displacements. The degradation in dilation and post-peak strength along asperities is modelled on the basis of the wear process. Then, geometric conditions and rock strength are considered through the dimensional analysis. Experimental studies of direct shear tests have been conducted using triangular shaped asperities and the results are correlated with the model’s behaviour to demonstrate its performance. The proposed joint model can be readily implemented in numerical procedures such as discrete element method and used to simulate block or panel caving.
Block cave mining has drawn increasing attention in recent years because it permits the bulk extraction of low grade ore bodies in a cost effective manner. The cave propagation of a jointed rock mass is strongly governed by the frictional characteristics of the geological discontinuities and in particular, joints in rock. Therefore, explicit and accurate formulation towards the shear behaviour of joints avails prediction of rock mass caving.
Amongst many contributing factors, surface roughness plays a key role in the friction between joint walls. On one hand, roughness dilatancy serves as an important stabilizing effect. Two contacting bodies tend to separate during tangential movement due to the sliding of asperity surfaces of one body on the other. When the increase in contact surface volume is constrained, dilatancy augments normal stresses compressing joint walls, which in turn, can significantly increase a joint’s resistance. The asperity surfaces responsible for dilation, however, will degrade and affect the subsequent shear behaviour depending on the normal stress level and the mount of sliding.
Goldstein et al and Patton  are among those who first attempted to predict the shear strength of non-planar rock joints based on the dilation caused by asperities. Thenceforth, the dilative feature of rock fractures has been addressed in both empirical and theoretical approaches by numerous researchers such as Ladanyi and Archambault , Barton , Schneider , Leichnitz , Plesha , Jing et al, Wibowo  and Oh et al.
The joint surfaces are irregular in nature; the roughness degree has been interpreted using statistical and fractal approaches [11-19]. As joint asperities degrade in shear, the surface damage has been investigated by several researchers based on the aforementioned methods including Gentier et al, Homand et al, Grasselli and Egger , Belem et al and Jiang et al. It seems that complete descriptions on asperity degradation are absent from those models because only geometric changes are taken into account. However, other factors such as normal stress magnitude and material strength are closely associated with the surface damage [25-28].
This paper presents a tribological relationship for joint asperity degradation based on the theory of wear. By dimensional analysis, factors affecting asperity deterioration including the applied stress and joint strength are taken into account. Examples are considered comparing the proposed model to experimental data.