Collapse mechanism of shallow tunnel based on nonlinear Hoek–Brown failure criterion

Collapse shape of shallow circular tunnel is derived using a new curved failure mechanism within the framework of upper bound theorem. Nonlinear Hoek–Brown failure criterion is adopted in the present analysis. With the consideration of supporting pressure, the energy dissipations of the new failure mechanism are calculated by employing integral technique. Equating the rate of energy dissipation to the external rate of work, the objective function is formulated, and is optimized with the variational approach. Numerical results are presented, and collapse mechanisms of shallow tunnel taking into account supporting pressure are obtained. The present results are compared with the previous solutions, and the agreement shows that the present method is valid. The effects of different parameters on the failure mechanisms are discussed, and a critical depth expression is proposed for classifying shallow and deep tunnels.

► In practice, many tunnels are shallow, and are subjected to supporting pressure. ► A new failure mechanism is proposed for shallow tunnels with the consideration of supporting pressure. ► The critical depth for classifying shallow and deep tunnels is established. ► The width of the failure block increases as the supporting pressure increases.