Probabilistic seismic demand models for circular tunnels subjected to transversal seismic load

This paper proposes convenient probabilistic models to estimate the seismic demands of circular tunnels to transversal seismic load. The uncertainties in the earthquake intensity, seismic load, and calculation methods are fully considered. Peak ground velocity PGV is selected as an essential earthquake intensity parameter because it is more correlated with the earthquake damage of underground structures, and a probabilistic model of PGV is proposed. Because the seismic response of tunnel linings is highly correlated with the free-field ground deformation, the maximum free field shear strain g_max is selected as the seismic load parameter. A probabilistic model of g_max is developed based on a series of seismic site response analyses. PGV plays a key role in the estimation of g_max. The analytical methods have been proposed to estimate the seismic response of tunnels. However, the results are usually biased, and the underlying uncertainties have not been well studied. To obtained unbiased seismic response estimates and capture the uncertainties in the calculation methods, the probabilistic seismic demand models are constructed by developing correction terms to the analytical method. The maximum moment M_max, thrust T_max, and diametric distortion Δd/d_max of the tunnel lining are considered. A pseudo-static analysis approach is used to simulate the seismic response of tunnels, and Bayesian updating is used for the model optimization and parameter estimation. The results of this paper can be used in the seismic design and reliability analysis of circular tunnels.