A New Unified Solution for Circular Tunnel Based on a Four-Stage Constitutive Model considering the Intermediate Principal Stress

Based on the triaxial test, the elasto-perfectly plastic strain-softening damage model (EPSDM) is proposed as a new four-stage constitutive model. Compared with traditional models, such as the elasto-brittle-plastic model (EBM), elasto-strain-softening model (ESM), elasto-perfectly plastic model (EPM), and elasto-peak plastic-brittle plastic model (EPBM), this model incorporates both the plastic bearing capacity and strain-softening characteristics of rock mass. Moreover, a new closed-form solution of the circular tunnel is presented for the stress and displacement distribution, and a plastic shear strain increment is introduced to define the critical condition where the strain-softening zone begins to occur. The new analysis solution obtained in this paper is a series of results rather than one specific solution; hence, it is suitable for a wide range of rock masses and engineering structures. The numerical simulation has been used to verify the correctness of the EPSDM. The parametric studies are also conducted to investigate the effects of supporting resistance, residual cohesion, dilation angle, strain-softening coefficient, plastic shear strain increment, and yield parameter on the result. It is shown that when the supporting resistance is fully released, both the post-peak failure radii and surface displacement could be summarized as EBM > EPBM > ESM > EPSDM > EPM; the dilation angle in the damage zone had the highest influence on the surface displacement, whereas the dilation angle in the perfectly plastic zone had the lowest influence; the strain-softening coefficient had the most significant effect on the damage zone radii; the EPSDM is recommended as the optimum model for support design and stability evaluation of the circular tunnel excavated in the perfectly plastic strain-softening rock mass.