Rock failure with weak planes by self-locking concept

In order to investigate failure of a rock mass having planes of weaknesses, a three-dimensional model is proposed based on the self-locking concept in friction analysis. In the case of two-dimensional problems, the model gives the same results as that of the Mohr–Coulomb criterion. The three-dimensional model can be reduced to the two-dimensional model, if the weak plane is parallel to the intermediate principal stress and/or the intermediate stress is equal to the minimum principal stress. The results indicate that the influences of three principal stresses and mechanical parameters of the weak plane on spatial failure region are remarkable, in terms of shape and range, that the spatial failure region becomes smaller as the mechanical parameters increases, and the weak plane will never fail when some threshold of mechanical parameters is reached, no matter what values of weak plane strike and dip will be. The spatial failure region becomes smaller with increased values of the intermediate and minimum principal stresses, conversely it becomes larger with the maximum principal stress increased. Additionally, the influence of bottom hole pressure on the failure range of weak plane is analyzed, for bore holes in naturally fractured formations, with the help of a local coordinate system.