The Stability Analysis of Tunnel Lining Structure with Seismic Excitation Based on the Energy Evaluation Principle

Earthquakes are vibrations induced by the rapid releases of large quantities of energy from the crustal movements. During seismic excitation, there are kinetic energy, damping energy, and strain energy acting on the tunnel structure. Based on the indexes of the total energy, releasable elastic strain energy, and dissipated energy, this paper proposes three energy evaluation criteria for the tunnel structure, which are applied to the optimization of the aseismic design of the cross-sectional shape and material property of the tunnel structure. It can be concluded that the peak values and accumulated values of elastic strain energy at the spandrel and arch springing are significantly larger than other positions, which indicates that the strengths of the spandrel and arch springing are the most influential factor for the seismic damage of the tunnel structure. Considering this factor, the width-to-height ratio of 1.33 and Poisson’s ratio of 0.3 are determined as the most optimal cross-sectional shape and material property, respectively. Furthermore, by analyzing the relationship between the internal energy and the input energy of the tunnel structure with seismic excitation and proposing an equation for the evaluation of the dynamic stability of tunnel structure, the stabilities of the tunnel structure with different PGAs are analyzed; it can be concluded that the larger the peak value of seismic wave acceleration, the longer the instable period and the greater the degree of dynamic instability. The derived equations can be used as references for the seismic analysis of the tunnel structure, and the conclusions of this paper can contribute to the aseismic design of tunnel lining.