An analytical Solution for Deep Circular Tunnels in Rock Based on GZZ Criterion

Tunnels in rock are often used for transportation, mining, and storage. It is important to perform accurate analysis and design so as to ensure the safety of tunnels during construction and operation. Currently, most of the analysis and design methods of tunnels in rock are based on the Hoek-Brown criterion, which ignores the effect of the intermediate principal stress (i.e., the three-dimensional (3D) strength) and might underestimate the rock strength. In this regard, this paper presents a new analytical solution for deep circular tunnels in rock with consideration of disturbed zone and 3D strength. The rock is assumed to be elastic-brittle-plastic and governed by a 3D Hoek-Brown yield criterion, the newly modified generalized Zhang-Zhu (GZZ) criterion. Based on the equilibrium equation, constitutive law, and large-strain theory, the governing equations for the stresses and radial displacement around the tunnel were derived and solved by using the programming language MATLAB. The proposed solution was validated by using it to analyze a tunnel and comparing the results with those from numerical analysis using commercial software FLAC3D. Finally, extensive parametric studies were performed on tunnels in both poor-quality and good-quality rock masses with a special focus on stresses and radial displacement of the rock mass. The proposed analytical solution can be used for the preliminary analysis and design of tunnels in different rock masses with the consideration of 3D strength.