Analytical and numerical approach for tunnel face advance in a viscoplastic rock mass

• Analytical approach by the integration of the rock–lining interface differential equation.
• Numerical technique to integrate an elastoviscoplastic law with energetic damage criterion.
• Numerical approach for tunnel excavation & lining mounting to analyze some different parameters.
• Simulation of 3D aspect of the tunnel face advancing and the lining installing.
• Comparison of the numerical and analytical results with a good agreement is obtained.

This paper presents both a numerical and an analytical approach for tunnel excavation and support mounting. The three-dimensional aspect of the tunnel face advance and the lining installation is simulated by a two-dimensional study assuming the hypothesis of gradual decompression of the primary stress on the outline of the tunnel. The numerical approach consists of a tunnel axis in an elasto-viscoplastic rock mass and a concrete elastic lining. This study emphasizes some important factors that influence the tunnel calculation, such as tunnel face, history of excavation phases, timing of the lining mounting, lining stiffness, and depth of the tunnel. The analytical approach is based on the determination and integration of the rock–lining interface differential equation. The author presents the analytical solution for (a) constant and non-constant lining pressure, and (b) taking into account the tunnel face influence. The comparison of the numerical results with the analytical solution is performed, and a good agreement is obtained.