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A numerical stepwise approach for analysis of cavity expansion in strain-softening rock or soil mass

Feng Wang, Mingyao Xia, Jinfeng Zou


This paper presents a numerical stepwise approach for analysis of cavity expansion in strain-softening rock or soil mass compatible with a linear Mohr–Coulomb or a generalized Hoek–Brown failure criterion. The conditions of the axisymmetric, plane strain and un-drained conditions are assumed for the cavity expansion problem. The initial in situ stress is assumed to be hydrostatic. In the presented approach, the plastic region is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium and compatibility equations, and the material parameters of the rock or soil mass are assumed to be the same in everyone ring. For the strain-softening behavior, it is assumed that all the strength parameters are a linear function of deviatoric plastic strain () for each rings. The increments of stress and strain for each rings are calculated with the finite difference method. The assumptions of the large strain for soil mass and the small strain for rock mass are adopted, respectively. Solutions of limited pressure and plastic radius are obtained by the numerical stepwise approach. Comparisons are conducted to validate the correctness of the proposed solution with Vesic’s solution (1975). Numerical examples are also carried out to highlight the influence of the strain-softening characteristic on the stress and displacement.


cavity expansion, strain-softening, numerical stepwise approach, un-drained condition, rock or soil mass

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