Analytical solution of equivalent stiffness of shield tunnel with consideration of incorporating combined action of longitudinal channel steel and axial force

To accurately and quickly predict the effect of longitudinal channel steel reinforcement technology on the equivalent stiffness of a shield tunnel, theoretical research is conducted on the longitudinal channel steel reinforcement technology. A new analytical solution is proposed for the equivalent bending stiffness of shield tunnel with consideration of incorporating combined action of longitudinal channel steel and axial force. The solution can degenerate into a special case with no longitudinal channel steel, which is consistent with classical theory, model test and numerical simulation, and validates the model and solutions. The results show that the neutral axial φ of shield tunnel decreases with increasing in longitudinal channel steel and longitudinal axial force, directly affecting the contact state between tunnel segments, which will impact the equivalent stiffness of the shield tunnel. The equivalent stiffness of a shield tunnel increase nonlinearly in an S-curve with the longitudinal axial force and decrease with an increasing bending moment, which is directly proportional to the tunnel segment width, the number of channel steel, the elastic modulus of channel steel, and the section area of channel steel. The influential order on the equivalent stiffness of shield tunnel is the number, section area, and elastic modulus of longitudinal channel steel. The influence mechanism of sensitivity parameters of longitudinal channel steel on the equivalent stiffness of a tunnel is theoretically explained in this paper, which enables accurate and quick prediction of the reinforcement effect of longitudinal channel steel.