Practical estimate of deformations and stress relief factors for deep tunnels supported by shotcrete

Even though ground-support interaction in the vicinity of the tunnel face is a typical 3D problem, tunnel support design is usually based on simplified plane strain models, which are strongly dependent on the assumed degree of ground stress relief at the time of lining installation. The paper focuses on tunnels supported by shotcrete close to the face, where the interaction between the loading process and progressive hardening of the green shotcrete makes the problem time-dependent. A constitutive law characterized by the time-dependent stiffness and strength of the shotcrete is employed herein. The results of an extensive parametric study based on 3D axisymmetric models are presented in the form of non-dimensional design charts, which can provide guidance to a preliminary evaluation of convergences and support loadings. Moreover a strategy is proposed to enhance the capability of simplified design methods (2D models, Convergence-Confinement Method). This consists in a "guided estimate" of stress relief factors, which again is based on the results of 3D time-dependent analyses. Finally, by way of example, the proposed method is applied to two well-documented case-histories.