Ground reaction curves for strain-softening rock masses with ground reinforcement based on unified strength criterion

• A novel analytical model integrates strain-softening behavior and intermediate principal stress to predict ground reaction curves for reinforced tunnels, overcoming limitations of existing models. • Existing models overestimate reinforcement effects; deformation prediction errors can exceed 75% when using single geological material models. • Neglecting softening and residual zones in natural regions leads to errors over 50%, highlighting the need for accurate constitutive modeling. • Incorporating intermediate principal stress reduces tunnel deformation by at least 30%, offering significant cost savings in reinforcement and support.