Analytical approach to the creep and hydromechanical couplings around underground cavities

This paper deals with the time-dependent behavior of rocks in the vicinity of underground cavities. Our approach is analytical and addresses different stages of the life cycle of a cavity. The theoretical framework is taken up from previous works [1-4] and completed to account for an irreversible viscoplastic behavior, which has been experimentally evidenced [5-9]. Other attempts to account for creep are available in the literature. Some of them use the viscoplasticity theory [10-14 for instance]. Most often, they require numerical tools. However, analytical approaches are useful to check the consistency of more complex numerical simulation and to make it possible to obtain practical estimations of the behavior of underground structures. To our knowledge, Pouya [13] provided an approximate analytical solution in the case of an unlined tunnel accounting for a monophasic rock mass obeying to a Norton-Hoff's creep law in the particular case of incompressible elasticity (v = 0.5). Cosenza et al. [14] analytically dealt with the long-term behavior of a spherical cavity inside a saturated poro-viscoplastic rock mass in the borderline case of stationary state, neglecting the transitional stages