Elastoplastic Semi-Analytical Solution for Deep Tunnels in Strain-Softening Rock Mass Considering Intermediate Principal Stress and Dilation Behaviour

Reliable estimation of squeezing deformation in deep soft-rock tunnels requires an elastoplastic formulation that can capture the post-yield response of the surrounding rock. However, existing theoretical approaches rarely account for the variation in intermediate principal stress associated with the evolution of dilatancy in strain-softening rock masses. To address this issue, a semi-analytical formulation is established using the modified GZZ strength criterion, in which the intermediate principal stress coefficient evolves with the dilatation angle. The proposed method is verified against published solutions and further evaluated using field data from the Xinhua Tunnel. The results indicate that the progressive decrease in dilatation angle toward the tunnel wall increases the intermediate principal stress coefficient, thereby enhancing the bearing capacity of the yielded rock mass and limiting both strength degradation and squeezing deformation. The predicted tunnel deformation agrees more closely with the field measurements than that obtained using approaches with a constant intermediate principal stress coefficient. Parametric analyses further show that dilatancy has a stronger influence on squeezing deformation in weaker rock masses and under higher geostress, whereas increasing support pressure reduces this influence.