A numerical procedure for the fictitious support pressure in the application of the convergence–confinement method for circular tunnel design

• Propose a numerical procedure for fictitious support pressure on a circular tunnel.
• Solve fictitious support pressure by coupling the GRC and LDP.
• Consider perfectly-plastic, brittle-plastic, and strain-softening rocks.
• Fictitious support pressure increases with critical softening parameter grows.
• Strong dilatancy behaviour reduces the stability of rock ahead of tunnel face.

In the vicinity of a tunnel face, the fictitious support pressure represents the support pressure acting on the periphery of the tunnel provided by the rock mass itself. It is an indicator of the self-supporting capacity of the rock mass.This paper aims at solving the fictitious support pressure on a circular tunnel with hydrostatic initial stress field. A numerical procedure for the fictitious support pressure is proposed for the elastic-perfectly-plastic, elastic-brittle, and strain-softening rock masses. The procedure is composed of two steps: first, the ground reaction curve (GRC) and the longitudinal deformation profile (LDP) are solved by a modified numerical approach; in this step, the finite difference method is utilised to derive the strain components, the stress components, and the radius of the plastic zone; then, by coupling the GRC and LDP, a fictitious support pressure is obtained by a simplified approach. By using the proposed procedure, the influencing factors of the fictitious support pressure, such as the critical plastic softening parameter, the rock mass quality, the dilatancy angle and the initial stress condition are studied individually. The results indicate that the effect of the critical plastic softening parameter on the fictitious support pressure, especially for the rock mass with good quality is obvious. For a rock mass with strong dilatancy behaviour, the fictitious support pressure ahead of the tunnel face decreases rapidly. The elastic assumption of the rock mass behaviour will underestimate the stress relief factor by a large extent.