A constitutive model to study frictional behaviour of rock joints has been constructed. Rock joints are treated as two rough surfaces in contact under normal and shear loads. The state of asperity contacts evolve from partially to fully sliding as shear load increases. The model shows that this critical slip distance D(I) is the distance at which the majority of contacts have changed from partially sliding to fully sliding. We argue that D(I) is equivalent to D(C), the critical slip distance for seismic instability, and here explore their scaling with models of fractal surfaces. The synthetic spectrum method has been used to generate fractal surfaces on different scales. D(I) has been calculated for these synthetic fractal surfaces with the contact model. It is found that D(I) is mainly controlled by the uncorrelated part of surface topography. The relationship between D(I) and the critical correlation length of the surface is a power law. If D(I) for natural faults is in the range of 1 mm to several cm, then the calculations show that the surfaces have correlation lengths of 10s to 100s of meters.
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