Numerical simulation of excavation in rock masses with the Hoek-Brown criterion

We propose here to develop a numerical method to simulate the behaviour of a rock mass during excavation. We use the Hoek-Brown criterion which is a good representation of the rocks and rock masses behaviour. We developed a steady-state algorithm which considerably reduces the calculation time so the plastic strains with the Hoek-Brown criterion can be solved in reasonable time. In the steady-state algorithm, the referential of the observer is in movement with respect to the applied load and we suppose the steady-state is reached. The hypothesis are a constant advancement rate and a section far enough from the entrance. Plastic strain are calculated using a projection algorithm, and then transported from each Gauss point to the next along each parallel to the advancement direction. We use a projection algorithm on the yield surface to obtain the plastic strains. The closest point projection is used for associated materials, and this method is updated with the dilatancy angle as a parameter to fit with non associated materials. We use 3-dimensions smooth versions of the Hoek-Brown criterion, where the initial hexagonal shape function is replaced by smooth shapes functions. With this numerical simulation, we can obtain the convergence profile of the excavation which depends on the ground behaviour. With this curve we can compare the effects of the material characteristics and determine the ground state in a given distance after the tunnel face.