A multi-scale model for longitudinal seismic design of prefabricated utility tunnel based on multi-point constraints

A multi-scale model for the longitudinal seismic analysis of underground prefabricated utility tunnel was proposed. In this multi-scale model, beam elements were used to model the utility tunnel segments, shell elements were used to model the weak parts, e.g., tunnel intersections, and node frames with multiple springs were used to simulated the behavior of the tunnel joint. The node frames, whose form are the same as that of the prefabricated joint, were established on a basis of the cross-sectional size and the joint form of the tunnel. By arranging multiple sets of nonlinear springs to connect adjacent node frames, the refined model of the utility tunnel joint was established. Based on the multi-point constraint method, the multi-point constraint equations between the structure model and the refined joint model were given. Finally, a specific straight utility tunnel as well as a specific cross-type utility tunnel were taken as the examples to verify the accuracy and applicability of the proposed model. The results indicate that the proposed model is suitable for the longitudinal seismic analysis of the utility tunnels with asymmetric cross-section and intersections, and may provide reference for the longitudinal seismic design of large-scale utility tunnels.