Design equation for stability of shallow unlined circular tunnels in Hoek-Brown rock masses

Safety assessment is one critical issue for constructions of tunnels and requires a reliable and accurate stability analysis. At present, a large number of researches in stability analyses of tunneling in rock masses have been conducted; however, a lack of an accurate and reliable design equation for the tunnel stability prediction is obvious. This paper presents a new design equation for stability analyses of shallow unlined circular tunnels in rock masses obeying the Generalized Hoek-Brown failure criterion. Because of the complexity of the problem’s nature, a closed-formed analytical solution of the problem is not possible to be achieved. Hence, the computational framework of the finite element limit analysis is selected to numerically derive the upper and lower bound solutions of the problem. A complete set of the dimensionless parameters covering the shallow cover-depth ratios of tunnels, the normalized uniaxial compressive strength of intact rocks, and the Hoek-Brown material parameters are comprehensively investigated. A new design equation for stability analyses of shallow unlined circular tunnels in rock masses is developed by employing a nonlinear regression analysis to the numerically derived average bound solutions. It is found that the proposed new design equation is highly accurate and provides a convenient and reliable tool for stability analyses of shallow unlined tunnels in rock masses in practice.