Empirical Response Spectra and Local Seismic Response of Elements Using the Mod-ξ (Var) Approach

A novel system identification technique, named Mod-ξ (var), has been developed, implemented, and validated to analyze the seismic response of a three-dimensional reinforced concrete shear wall building during the mega-earthquake that struck central Chile in 2010 (Mw = 8.8). The Mod-ξ (var) method is an advancement of conventional Least-Square modal system identification techniques, which involves adjusting modal parameters within small data windows to accurately represent seismic data in both the frequency and time domains. This technique offers several advantages over traditional approaches. Firstly, it enables estimating time-variant dynamic properties during seismic events, allowing for a comprehensive understanding of the building’s response throughout the earthquake. Additionally, it facilitates the reliable assessment of continuous nonlinear modal responses, and empirical response spectra associated with each seismic input can be determined, providing valuable insights into the structural behavior under different earthquake scenarios. Moreover, the technique enables calculating local responses for measured and unmeasured floors. This is achieved by multiplying the nonlinear modal responses obtained from the Mod-ξ (var) approach with all building floors’ normalized seismic mode shapes. These mode shapes can be estimated using ambient vibration tests. Finally, the seismic floor deformations obtained from the Mod-ξ (var) approach can be applied to a Finite Elements Model. This allows for evaluating important engineering quantities such as inter-story drift, inter-story forces, and local demands on structural elements. Parameters like drift ratios, curvatures, internal forces, stresses, and strains can be determined, providing crucial information for structural analysis and design.