Probabilistic density evolution analysis of dynamic response of tunnels under stochastic earthquakes

Due to the stochastic characteristics of ground motion, it is difficult for the deterministic method to completely consider the complex stochastic characteristics of ground motion. It is of great practical significance to study the seismic response of tunnel structures by using the stochastic analysis method for the seismic design of underground structures. In this study, the research object is a typical circular tunnel structure in soft soils. First, a nonlinear interaction analysis model for the underground soil tunnel in a typical project site is established. Then, a random seismic model is used to generate a non-stationary seism that matches the requirements of the seismic design code. A probability density evolution analysis method is introduced into the seismic analysis of the tunnel structure, which initially explores the evolution characteristics of the probability density of its seismic performance. Using the tunnel inclination angle as the seismic performance index, the probability density function of the tunnel structural response is solved by using the probability density evolution method, and the exceedance probabilities of the tunnel inclination angle are obtained when the tunnel has no damage, slight damage, moderate damage and severe damage. The results show that the exceedance probabilities of the tunnel inclination angle in the four damage states are 98.88%, 86.10%, 30.90% and 3.70%, respectively. The proposed probability density evolution method can accurately obtain the instantaneous probability information of the tunnel inclination angle, and provide a new prospect for the study on the probability evolution characteristics of seismic performance of the tunnel structures.