Micromechanical basis for shear strength of rock discontinuities

• Theoretical bases allow to elaborate a strength criterion for discontinuities.
• A three-dimensional study is performed for joints with spherical cap irregularities.
• The theoretical formulation is applied to the Hoek and Brown failure criterion.
• Analysis of the results allows the explanation of the Barton empirical formula.

The theoretical basis for evaluating shear strength in rock joints is presented and used to derive an equation that governs the relationship between tangential and normal stress on the joint during situations of slippage between the joint faces. The dependent variables include geometric dilatancy, the instantaneous friction angle, and a parameter that considers joint surface roughness. The effect roughness is studied, and the aforementioned formula is used to analyse joints under different conditions. A mathematical expression is deduced that explains Barton׳s value for the joint roughness coefficient (JRC) according to the roughness geometry. In particular, when the Hoek and Brown failure criterion is used for a rock in the contact with the surface roughness plane, it is possible to determine the shear strength of the joint as a function of the relationship between the uniaxial compressive strength of the wall with the normal stress acting on the wall. Finally, theoretical results obtained for the geometry of a three-dimensional joint are compared with those of the Barton׳s formulation.