Ground response curves for rock masses exhibiting strain‐softening behaviour

Abstract

AbstractA 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. Copyright © 2003 John Wiley & Sons, Ltd.