Upper bound solution to the support pressure of tunnels excavated in weak Hoek–Brown rock masses

Determining a reliable value of the support pressure is necessary to prevent tunnel instability during excavation in weak rock masses. There are a few appropriate analytical solutions, most focused on tunnels excavated in soils. The present study proposes a method for determining the support pressure required to stabilize tunnels excavated in weak rock masses. The upper bound limit analysis method was applied for a rock mass obeying the Hoek-Brown failure criterion. Based on the findings, improving the strength of the rock masses results in decreasing the required support pressure. Increasing the Hoek-Brown parameters m_i from 5 to 20, GSI from 10 to 25, and σ_ci from 1 to 10 MPa, results in a maximum reduction of the tunnel support pressure by 62%, 56%, and 70%, respectively. In addition, increasing the ratio of horizontal to vertical insitu stresses from 0.4 to 1.2 reduces the maximum support pressure by about 59%. Moreover, increasing the disturbance factor from zero to 1 results in an increase of about 135% in the support pressure, while by increasing the tunnel width and the unit weight of the rock mass surrounding the tunnel, the maximum increase of 181% and 93% were observed in the support pressure.