According to the features of tunnel engineering

interaction between tunnel and wall rock is considered. Based on structural dynamics theory

interaction theory and the idea of equivalent radius

a dynamic equilibrium equation of tunnel structure is established. The equation takes into account the action of inertial force of the tunnel structure. As can be seen from the equation

classical displacement response method is a special case of the method. Factors effecting on longitudinal stress of tunnel lining have been studied. Those factors contain tunnel depth

strata shear wave velocity

shear wave direction

elastic foundation coefficient

elastic modulus and the characteristic period of the overlying strata. The case studies show that: (1) Interaction between structure and wall rock has a greater impact on lining. Without considering the interaction

the results are relatively conservative. (2) Inertial force has a great effect on the ultra shallow structure; but with the tunnel depth increases

the impact of inertial force can be neglected. (3) The method is actually an engineering algorithm for solving tunnel longitudinal stress. In the preliminary design of tunnel

the method could provide theoretical reference for seismic concept design of the overall tunnel.