Elastic perfect plastic rock mass analysis and equivalent GSI determination considering strain-softening behavior and three-dimensional strength

The elastic perfect plastic model (EPP) fails to accurately capture the strain-softening mechanical behaviors of rock masses, while the post-peak constitutive model of elastic strain softening (ESS) has great application limitations in practical engineering for complex numerical algorithms. In this paper, an EPP constitutive approximation of rock mass considering three-dimensional strength and strain-softening characteristics is proposed. The forward analysis method of the equivalent Geological Strength Index (GSIeq) is given considering the impact of in-situ stress, rock mass properties and engineering excavation. Extensive case studies demonstrate that the radial stress and displacement obtained by the proposed method agree well with those of the ESS model, with only small errors in the Ground Response Curve. The rock mass elastic modulus E and the initial stress level p0 significantly affect GSIeq, while the support pressure ps contributes little to that. As Rp,EPP/R0 > 3.0, usually GSI < 25, the residual strength parameter GSIr can be directly used as the calculation parameter of the EPP model, while for a highly qualified rock mass, such as GSI > 75, the peak strength parameter GSIp can be directly used as an approximate value of GSIeq. Furthermore, with the increase of the in-situ stress level, GSIeq gradually decreases to GSIr, and the difference of plastic stress distribution law based on ESS and EPP models gradually diminishes. Moreover, the proportion of plastic deformation to total deformation increases nonlinearly with buried depth. The proposed method offers a new calculation idea for the simplified analysis of strain-softening rock masses.