In order to quickly and accurately evaluate the effect of longitudinal compressive pressure and reinforced steel plate on the mechanical properties of shield tunnel

we established stress equilibrium equations that consider the coupling effect of longitudinal pressure

bending moment and reinforced steel plate based on the joints of shield tunnel lining

and finally derived the analytical solution. The feasibility of the method was confirmed by comparing with the results of classical equivalent bending stiffness and numerical simulations. The results indicate that the neutral axial decreases with the increasing longitudinal pressure

thickness and elastic modulus of the reinforced steel plate. The equivalent bending stiffness of the shield tunnel decreases with the increasing bending moment (maximum and minimum equivalent bending stiffness are independent of the bending moment). It follows an S-curve pattern correlation with the longitudinal pressure

and shows a nonlinear correlation with the thickness and elastic modulus of the reinforced steel plate. The equivalent bending stiffness of the tunnel with reinforced steel plate is 6.58 times that of the tunnel without steel plate. The bending bearing capacity is nonlinear with respect to the longitudinal pressure

the thickness and elastic modulus of reinforced steel plate. The opening of tunnel lining joints is nonlinear with respect to the bending moment

but inversely nonlinear to the longitudinal pressure

the thickness and elastic modulus of the reinforced steel plate. This analytical solution reveals the evolution of the mechanical properties of shield tunnels under the influence of longitudinal pressure and reinforced steel plate.