Analytical solution for equivalent stiffness of shield tunnels under combined action of longitudinal channel steel and axial force

To accurately and quickly predict the effects of longitudinal channel steel reinforcement technology on the equivalent stiffness of a shield tunnel, the theoretical researches are conducted on the longitudinal channel steel reinforcement technology. A new analytical solution is proposed for the equivalent bending stiffness of the shield tunnel under the combined action of longitudinal channel steel and axial force. The solution can be degenerateed into a special case without longitudinal channel steel, and it is validated those the classical theory, model tests and numerical simulation. The results show that the neutral axial φ of the shield tunnel decreases with the increasing 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 the shield tunnel increases nonlinearly in an S-curve with the longitudinal axial force and decreases with the increasing bending moment, which is directly proportional to the width of tunnel segment, the number, elastic modulus and sectional area of channel steel. The influential order on the equivalent stiffness of the shield tunnel is the number, sectional area and elastic modulus of longitudinal channel steel. The influence mechanism of sensitivity parameters of longitudinal channel steel on the equivalent stiffness of tunnels is theoretically explained, which enables accurate and quick prediction of the reinforcement effects of longitudinal channel steel.