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Due to the excavation or reinforcement of tunnels, the properties of the rock mass close to tunnels can be significantly changed. To account this issue, a closed-form solution is presented to determine the induced stresses and deformations with consideration of the effects of the altered zone around a circular tunnel and of the self-weight of different zones. For this purpose, the Mohr–Coulomb criterion and the elastic–brittle–plastic model are assigned to both the altered zone and the initial rock mass. Due to the different properties of these zones, the plastic zone can be initiated from the altered zone, the initial rock mass, or both of them simultaneously. By gradually decreasing the internal support pressure, it can be expected that the stresses satisfy the failure criterion. Investigating possible conditions, it can be seen that six different cases can exist. These cases were analysed, and the code of which was written in the MATLAB software. After verifying the proposed procedure with the existing analytical methods, a parametric study was conducted. The results show that neither of the damaged zone nor the reinforcement zone can be neglected, and the propagation of the plastic radii must be considered.

Ground reaction curve of a circular tunnel considering the effects of the altered zone and the self-weight of the plastic zones