Convergence of circular tunnels in elastoplastic rock masses with non-linear failure criteria and non-associated flow laws

This work provides new findings on the theory of non-associated plasticity applied to the study of convergence in tunnels. It focuses on elasto-plastic rock masses with linear and non-linear strength criteria and associated and non-associated flow laws. It seeks to obtain the “Characteristic Rock mass Curve” based on the “Convergence–Confinement” method. The results that are obtained are compared to other calculation procedures. Detailed mathematical expressions are proposed for implementation in a computer spreadsheet.

► A mathematical procedure has been developed to obtain the convergence curve.
► Based on the theory of the plasticity, this work proposes a general expression.
► Formulation valid for any failure criteria and for any type of plastic flow law.
► Expression has been obtained for the Mohr–Coulomb criterion and the Hoek–Brown failure criterion.
► Expression has been obtained for the linear flow law.