Deformation and stress of tunnel structures based on modified longitudinal equivalent continuous model

It is of great importance for guaranteeing the metro operation safety to promptly grasp the condition of deformation and stress of tunnel structures. A new modified longitudinal equivalent continuous model for shield tunnels is established based on the conventional one by taking into consideration the lateral rigidity, influence scope of annular gap and bolt pre-stress. Subsequently the equations for solving the equivalent longitudinal bending stiffness, the ultimate moment of tunnel and the maximal amount of joint opening under elastic and plastic states are derived respectively using to the modified model. Based on the engineering practice of Shanghai metro line 2, the influence laws of lateral rigidity and influence scope of annular gap on the equivalent longitudinal bending stiffness are analyzed. Finally, the formulae for longitudinal curvature radius, joint opening, segment stress and bolt tension are proposed according to five critical conditions of tunnel structures, and the corresponding critical indexes which can be used to diagnose the tunnel health are obtained.