基于切向应变软化的深埋圆形隧道围岩弹塑性分析

为了研究深埋圆形隧道围岩的应变软化行为，首先通过引入应变软化度，即软化区与残余区交界面处的切向应变和弹塑性交界面处的切向应变的比值，来表征应变软化程度。其次，推导了求解软化区与残余区位移方程，并将该方法求得的位移曲线与Lee法和Cui法对比，验证了方法的正确性。最后，通过算例分析，研究不同力学模型对塑性区半径的影响，以及应变软化度对塑性区中软化区与残余区比例和位移的影响。结果表明：弹塑性交界面处的围压与软化度和支护力均无关，塑性区半径与支护力有关；软化度直接影响软化区与残余区的比例，随着软化度的增加，软化区范围增加，相应的残余区范围减小；软化区与残余区交界面的位移随着软化度的增加而逐渐增加，应变软化度的增加，支护力对其影响增加；洞壁处的位移受支护力的影响较大，随支护力的增加而减小。

Elasto-plastic analysis of a deep circular tunnel based on tangential strain softening

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.