Time effect of stress and deformation of surrounding rock of circular tunnels during unloading

The stress state and deformation of surrounding rock of deep-seated tunnels are very important to design of underground engineering. With consideration of the stress concentration and relaxation induced by the nonuniformities, a series of equations for the surrounding rock follows in the deforming process, including the relationship between excess stress and nonuniformity size and unloading duration, is established to deduce the analytic expression of deformation of surrounding rock. The whole deforming process is divided into two stages: the unloading stage and the stress relaxation stage. And the approximate analytic expressions of stress and deformation are solved by successive approximation method. The solutions take the stress concentration and time effect of unloading into account; and they reflect the influence of nonuniformity and unloading duration on the stress and deformation of surrounding rock. Analytical results show that the local excess tensile stress concentrations appears in surrounding rocks in and after the unloading process; and the deformation have a additional increase after unloading.