An Extended Self-Similarity Numerical Algorithm for Strain-Softening Rock Models

The post-peak failure and softening mechanisms of surrounding rock in common tunnel, mine shaft, and roadway engineering primarily include radial tensile softening, shear sliding softening, and circumferential compressive–shear softening. Given the distinct post-peak failure and softening mechanisms, the softening coefficient in self-similarity analytical algorithms for stability analysis should differ accordingly. In this paper, to address the limitation of the existing self-similarity numerical algorithms for the deformation and failure of rock surrounding circular excavations—which typically employ only the plastic shear strain as the softening coefficient—we extend the self-similarity numerical algorithm by incorporating two additional softening coefficients: the maximum and minimum plastic principal strain. We validated the extended algorithm’s accuracy and reliability by comparing its stress, displacement, and plastic zone radius predictions with those obtained through numerical simulation and engineering monitoring and examined its sensitivity to step length variations under various softening coefficients and yield criteria. According to the validation and comparison with existing algorithms, the extended algorithm extends the applicability scope of the original self-similarity numerical algorithm and significantly improves the accuracy of the calculated results. Finally, using the extended algorithm, we systematically compared and quantitatively analyzed the stress, deformation, and failure characteristics around a circular excavation across different softening coefficient categories, including their critical values, revealing the influence patterns of the softening coefficients and their critical values on the stability of engineering surrounding rock.