Ground response curves for rock masses exhibiting strain-softening behaviour

E. Alonso, L. R. Alejano, F. Varas, G. Fdez-Mańin, C. Carranza-Torres

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294 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1153-1185
Number of pages33
JournalInternational Journal for Numerical and Analytical Methods in Geomechanics
Issue number13
StatePublished - Nov 2003


  • Ground response curves
  • Self-similarity
  • Strain-softening
  • Tunnels


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