Response spectrum method for spatial seismic ground motion

For seismic analysis of wide structures (for example, airports, stadiums, bridges, etc.), it is important to consider the wave seismic motion of the ground with spatial variability. The differential seismic motion is described by the vector field of kinematic parameters at each point of the base. The differential model of seismic excitation is used for structures on a flexible foundation or discrete supports, if the short-length waves (compared to the size of the foundation) are dominated in seismic waves spectrum. Such excitation is accompanied by angular displacements due to uneven translational ground motions, and it is not yet possible to consider using standard seismic analysis. This paper presents a method of differential seismic analysis with the corresponding modification of the response spectrum (RSM) method. The proposed method requires three accelerograms at each reference point. These accelerograms can be obtained during detailed seismic zoning. To illustrate the method, a model of a stadium cover is considered, for which it is important to apply a spatial differential seismic excitation, and some properties of the excitation are described and analyzed.