A new approach for analyzing circular tunnel in strain-softening rock masses

Although it is relatively a simple problem to study circular tunnels excavated in isotropic rock masses under hydrostatic stress fields, the results of stresses and displacements around circular opening can be insightful for ground support design and stability evaluation. Moreover, the solutions are useful in the validation of constitutive models and numerical codes. In the several decades past, many scholars studied this kind of problem in the Mohr–Coulomb (M–C) media, the Hoek–Brown (H–B) media and the generalized H–B media and considered the elastic–perfectly plastic, elastic–brittle–plastic and strainsoftening models with associated flow and non-associated flow rules. According to the existing literature surveys, most [1–13] of the researches are about elastic–perfectly plastic and elastic– brittle–plastic models because closed-form solutions (or numerical solution) can be easily obtained under certain assumptions. However, Hoek and Brown [14] suggest that the average quality rock masses behave in a strain-softening mode in the field of underground rock engineering. Therefore, it is of practical importance to study the mechanical behavior of normal rock masses with strain-softening behavior. By means of the classical theory of plasticity, materials with perfectly brittle–plastic and perfectly plastic constitutive model can be easily described and simulated in numerical methods such as the finite element method [15,16], etc. But it is more difficult to model the strain-softening material due to the negative slope in the stress–strain coordinates. Even for the above-mentioned excavation of circular tunnel in strain-softening materials, fewer attempts have been made [17–23] thus far. The reason is that the relationship among the stresses, plastic strain and the strength