Seismic Interferometry of a Soil-Structure Interaction Model with Coupled Horizontal and Rocking Response

This article presents a system identification analysis of a soil-structure interaction model with coupled horizontal and rocking response based on a combination of Fourier analysis, wave travel-time analysis, and a relationship between fixed-base, rigid-body, and system frequencies. The study provides insight into the coupling of the structural and soil vibrations useful for interpretation of seismic recordings in structures. The structural model captures one-dimensional shear-wave propagation in the structure. The analysis shows that the system functions with respect to foundation horizontal motion are those of the coupled soil-structure system, which differs from conclusions of earlier studies based on a model without foundation rocking. The energy of the system vibrational response is concentrated around the frequencies of vibration of the system, which depend on the properties of the structure, soil, and foundation. The analysis shows that the structural fundamental fixed-base (uncoupled) frequency f(1) is related to the wave travel time tau (from the base to the top) by f(1) = 1/(4 tau) and that accurate measurement of tau, unaffected by soil-structure interaction, can be obtained from impulse response functions, provided that the data are sufficiently broadband. This is an important result for structural health monitoring because it shows that structural parameters unaffected by soil-structure interaction (tau, as well as f(1) for structures deforming primarily in shear) can be estimated from seismic monitoring data with minimum instrumentation (two horizontal sensors, one at the base and one at the top). This extends the usability of old strong-motion data in buildings, most of which have not been extensively instrumented, and lessons that can be learned for development and validation of structural health monitoring methodologies. The presented results correspond to a model of the north-south response of the Millikan Library in Pasadena, California, which has become a classical case study for soil-structure interaction.