This work explores the implementation and applications of discrete-time filters as time-domain approximations of frequency-dependent foundation impedance functions for use in substructure dynamic response history analysis. The project's ultimate objective is to offer practicing engineers a robust, reliable option for accounting for inertial soil-structure interaction in time domain analyses.
The substructure method is a means of accounting for the interaction between a structure, its foundation, and the surrounding geology when subjected to dynamic excitation. The method models the soil-foundation interface using what are termed the foundation impedance functions. The frequency dependence of these functions complicates the method's implementation, especially in the time domain. Approximating impedance functions using discrete time filters yields recursive, time-dependent relations that may subsequently be incorporated into the system's equations of motion for integration using standard time-stepping methods.
Work along four interconnected lines of inquiry are presented. The first thread comprises a critical review of existing literature and delineates the motivation for the present effort. The second provides formulation and implementation details for both elastic and inelastic structural systems. Also included is a detailed analytical and numerical analysis of the stability of combined filter-integrator. The third line of effort includes three practical applications of the filter method, an investigation into the effects of inertial soil-structure interaction on yielding systems, a demonstration of the effects of soil profile on constant ductility spectra, and a case study wherein the filter method is used to predict the response of the Millikan Library on the campus of the California Institute of Technology to the 2002 Yorba Linda Earthquake. The final line of effort specifically targets practicing engineers by offering further detail on filter design and features a tutorial on filter design using the MATLAB programming environment.
