Ground response curves for rock masses exhibiting strain-softening behaviour

A literature review has shown that there exist adequate techniques to obtain ground reaction curves for tunnels excavated in elastic-brittle and perfectly plastic materials. However, for strain-softening materials it seems that the problem has not been sufficiently analysed. In this paper, a one-dimensional numerical solution to obtain the ground reaction curve (GRC) for circular tunnels excavated in strain-softening materials is presented. The problem is formulated in a very general form and leads to a system of ordinary differential equations. By adequately defining a fictitious 'time' variable and re-scaling some variables the problem is converted into an initial value one, which can be solved numerically by a Runge-Kutta-Fehlberg method, which is implemented in MATLAB environment. The method has been developed for various common particular behaviour models including Tresca, Mohr-Coulomb and Hoek-Brown failure criteria, in all cases with non-associative flow rules and two-segment piecewise linear functions related to a principal strain-dependent plastic parameter to model the transition between peak and residual failure criteria. Some particular examples for the different failure criteria have been run, which agree well with closed-form solutions - if existing - or with FDM-based code results. Parametric studies and specific charts are created to highlight the influence of different parameters. The proposed methodology intends to be a wider and general numerical basis where standard and newly featured behaviour modes focusing on obtaining GRC for tunnels excavated in strain-softening materials can be implemented. This way of solving such problems has proved to be more efficient and less time consuming than using FEM- or FDM-based numerical 2D codes.