By excavating an underground space, the state of stresses and displacements are changed in comparison to the initial state. This variation depends on the advancement of tunnel and rheological behavior of rocks. In this paper the effect of creep is discussed. Rock mass is assumed isotropic and homogenous. Tunnel is assumed to be circular and driven in hydrostatic stress field. The burger body which is able to model the primary and secondary creep regions of rock masses is applied. For the sake of simplicity, at first unlined section of tunnel which is too far from the face is studied. The differential equation corresponding to this case, is derived. Also analysis is performed for the section which is influenced by tunnel face. For further research, the effect of support system is also included in formulation. In this way, proposed analytical model is able to estimate the time dependent deformation of tunnel and the level of applied pressure upon support system. For verification, tunnel "Quatre chemins" in France is studied. The advancement of that tunnel was stopped for three days. The visco-elasic convergence of the tunnel wall was measured by convergencemeter. The derived formulation is applied for that case and the creep parameters of this tunnel are calculated. With these parameters the tunnel is numerically analyzed by FLAC code. The results of proposed analytical model showed a proper accommodation with the numerical analysis and the instrumented tunnel.
The ground pressure on the lining of tunnel increases with time. This is due to the advancement of tunnel face and time-dependent mechanical behavior of the surrounding medium. The effect of these two different factors must be separated . For circular tunnel in homogeneous and isotropic linear visco-elastic medium an analytical solution for convergence of tunnel walls was proposed by Panet . For similar problem, a closed-form solution for the pressure acting on support system was given by Sakurai . For sections which have distance up to two or three times the tunnel diameter from tunnel face (near sections from tunnel face), convergence induced mainly by face advance effect. Different empirical functions for considering this effect have been proposed [4, 5, 6]; however for far sections from tunnel face, the induced convergence is because of time-dependent properties of rocks (creep effect). The creep of rocks has been studied by many authors [7, 8, 9]. General form of the creep curve for rock is composed of three different regions. It is known that Burger body is adapted very well to the primary and secondary regions of creep curve. Kontogianni by studying two road tunnels in Greece establishes that more than 50% of total deformation tunnel is time dependent . Sulem et al,  have presented a closed-form solution for determination of wall displacements and ground pressure acting on tunnel supports. They have used Kelvin-Voigt model for considering the creep behavior of rocks.