Study of bifurcation in the problem of unloading a circular excavation in a strain-softening material

Abstract

Abstract This paper presents a study of bifurcation in the problem of unloading a circular excavation in a strain-softening rock mass. The analysis focuses on how bifurcation affects the calculation of ground reaction curves for tunnels. To begin with, the most important issues in strain-softening behaviour are discussed, with the concepts of bifurcation and localisation presented by reviewing physical observations of these phenomena in rocks and rock masses. Next, theoretical formulations and numerical approaches are briefly reviewed, and on this basis, a sufficiently good description of phenomena involved in bifurcation can be obtained using standard FDM or FEM codes with sufficiently fine meshes. A series of models of tunnels excavated in strain-softening materials were created and analysed using an FDM-based code, in which bifurcation and localisation could be clearly observed. These simulation results were compared with self-similar results, revealing that the effects of these phenomena are irrelevant when an appropriately large spatial scale, as in tunnels, is considered.