When an underground excavation is cut in a discontinuous rigid rock mass, instabilities may occur mainly due to block failure. Isolated rigid block methods were developed since the 80’s to locate critical blocks and evaluate their stability but have major drawbacks: ignoring in-situ stresses, mechanical behavior of joints and rotational movements. Other methods included those variables improperly and were limited to simple cases. This paper presents a critical review of previous approaches then a more complete model to study isolated rock blocks is proposed. It is based on the fact that stresses on the block faces are known before excavation and once a face is freed, the block moves as a rigid body in translation and rotation. Applying equilibrium and rock joint behavior equations, the stresses on the faces after excavation can be calculated and stability evaluated using a Mohr- Coulomb criterion. Any block geometry can be studied by partitioning the block faces into simple elements. Numerical integration is done on elements using Gauss points. The method is applied on a case study and comparisons are made with other simplified methods. Finally, a parametrical analysis shows the important influence of in-situ stresses and joint stiffnesses on the block’s stability.


When underground excavations are made in rigid rock masses intercepted by several discontinuities, blocks may form at the free surface and present the risk of sliding or falling into the open space causing damage. Modeling such phenomena is an essential requirement in order to predict a degree of instability and evaluate the support needed. Adopting a continuum model without discontinuities is not appropriate in this case since the main deformation occurs due to the displacements about the joints rather than to the deformation of the rock matrix. Furthermore, applying a complete discontinuous method, including all joints, is computationally hard because of the complexity of the three dimensional geometry. Additionally, the uncertainties concerning the distribution of joint sets require performing multiple simulations in order to cover all the possibilities. From the necessity to overcome this complexity, came the idea of studying separately only the blocks formed at the surface of the tunnel. Supporting the unstable blocks is assumed to assure stability for all the rock mass. This approach is simple and can provide the engineer with an easy tool to evaluate the stability of the excavation or to choose its optimum direction. The generation of blocks can be made by studying all the combinations of discontinuities that may form removable blocks at the surface of the tunnel. This approach does not require information of spacing between discontinuities or their exact location (ubiquitous approach). Another approach consists of generating all blocks by using distribution of joint sets or introducing joints one by one (specific approach). This article does not consider the problem of generation of the rock blocks in the rock mass. It focuses only on the stability analysis of a rock block once it is generated by whatever method. Isolated rock block methods have been widely used.

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