Semi-analytical solution for time-dependent deformations in swelling rocks around circular tunnels

Underground structures in swelling rocks bear time-dependent swelling effects. Upon excavation of underground spaces, the state of stresses and displacements change compared with the initial state. The stress and displacement variations depend on tunnel advance and the rheological behavior of surrounding rock mass. The swelling behaviour of rocks is known as a complicated phenomenon and very important task in tunnel design process. The paper aim is to predict the time-dependent displacement of the tunnel after the excavation has stopped or after installing the support system. The assumption is made that the medium around tunnel is both isotropic and homogenous. The section of tunnel is also assumed circular which in view of stress field, is excavated in Hydrostatic and non-hydrostatic conditions. A semi-analytical model on the basis of experimental results is adopted to evaluate the ground swelling strains as a function of time and stress. Given the current assumptions and conditions, a semi-analytical solution is derived to predict the time-dependent displacements and lining pressure for a circular shaped tunnel section in a swelling ground. Eventually, the model is loaded by an axisymmetric far-field pressure and the effect of the tunnel face on the lining pressure is also considered. On the whole, the comparison between modeling results and actual data, proved an accordance between them. As the results indicate, such parameters as, time dependent modulus of swelling and swelling strain coefficient as well as the initial aspect ratio, play a prominent role in controlling the swelling deformations. The set up time of lining is also considered as an impressing factor controlling the swelling pressure. In mediums of high swelling potential, the temporary support system installation has to be made to allow some ground deformations prior to the permanent support (lining) gets installed which causes the swelling deformation to get relieved.