Abstract: To explore the strain-softening behavior of a deep circular tunnel, the strain softening coefficient is introduced to characterize the degree of strain softening. This coefficient is defined as the ratio of the tangential strain at the boundary of the softening-residual plastic zone to the tangential strain at the boundary of the elasto-softening zone. Then, the displacement equations of the softening plastic zone and the residual plastic zone are deduced. The displacement curves calculated by the deduced method are compared with those calculated by Lee’s method and Cui’s method to verify its accuracy. Finally, using example analysis, the difference of the plastic radius is obtained due to the difference of the selected mechanical model. In addition, the effect of the strain softening coefficient on the ratio of the softening plastic zone to the residual plastic zone and displacement is analyzed. The results show that the confining stress at the elasto-plastic boundary is not related to strain softening coefficient and support force, but the plastic radius is related to the support force. The strain softening coefficient has a direct influence on the ratio of the radius of the residual plastic zone to the radius of the plastic zone. With the increase of strain softening coefficient, the range of softening area increases, leading to the decrease of the residual plastic zone. The displacement surrounding tunnel wall is greatly affected by support force and deceased with the increase of support force.

Key words: rock masses, strain softening coefficient, plastic radius, displacement