Modélisation de la stabilité des blocs rocheux isolés sur la paroi des excavations souterraines avec prise en compte des contraintes initiales et du comportement non linéaire des joints

Failure of rock blocks located at the surface of underground excavations is a common problem in discontinuous rock masses. Since exact methods that take into account all blocks and their interactions are computationally hard, the Isolated Blocks method is usually adopted. It consists in studying each block considering it to be rigid and the surrounding rock mass to be rigid and fixed. Nevertheless, none of the existing methods based on this approach takes into account initial stresses and joints behavior rigorously. In this thesis, a new method providing significant improvements to conventional Isolated Blocks methods is developed. Considering that initial stresses are known, the excavation process is modeled by unloading the block's free face. Stresses acting on the faces in contact with the rock mass are then resolved by taking into account force and moment balance equations, joints behavior and rigid body movement. This leads to a linear system where the block's translation and rotation vectors are the only unknowns.Two models are proposed: the first one assumes linear elastic joint behavior, thus the stability is evaluated a posteriori. The second, more realistic model, assumes joint behavior to be hyperbolic in the normal direction and elastoplastic in the tangential direction, while also accounting for dilatancy. This non-linear problem is solved numerically by explicit integration in the kinematic time with constant deconfining steps. Also, thanks to the surface integration technique used, any block geometry can be studied. The method proposed is validated and compared to other conventional methods. Parametric studies show the influence of initial stresses and the joints' mechanical properties on the stability. Rock support modeling is also integrated into the code. Finally, the new method is applied to study an assemblage of blocks around an underground excavation and is compared to a model that takes into account all the blocks with the Distinct Element Method. It is also used to reproduce an actual block failure case.