Multi-scale dynamic analysis method for underground structures

Underground structures suffered great damages frequently in recent earthquakes. A number of researchers have developed studies on seismic analysis of underground structures, but failed to address the existing multi-scale dynamic problems. In this paper, a multi-scale method is proposed for the dynamic response analysis of underground structures subjected to dynamic loadings. This method does not result in spurious wave reflections and does not need additional filtering or damping. Based on the bridging coupling theory, Lagrangian multipliers are introduced to append the constraints into the dynamic equations, and the dynamic control equations are deduced for the multi-scale subdomains using the energy potential function. Based on the central differential method, a multi-scale dynamic explicit algorithm is proposed to solve the established multi-scale dynamic coupling systems. As an application, the presented method is used in an existing underground structure. The advantage of the multiscale modeling method in minimizing spurious reflections is verified by providing comparisons with the displacement-coupled method. The research is of great benefit to seismic analysis theories and methods of underground structures, and also provides instructions for dynamic calculation and analysis of underground structures.