Abstract
The effects of dynamic soil–structure interaction (SSI) have been extensively studied in the last few decades, and proper analysis for the linear elastic case in frequency domain has been established successfully. However, SSI is rarely considered in the design of building structures, and instead, buildings are frequently analyzed using a rigid base assumption and quasi-static loading conditions that ignore SSI and its dynamic nature. Acknowledging these shortcomings, the National Institute of Standards and Technology (NIST) published in 2012 a set of recommendations on time-domain analyses of SSI for building structures compatible with standard finite element packages for consideration in engineering design. The so-called NIST GCR 12-917-21 report introduced a major simplification to enable frequency domain tools to be implemented in time domain analyses. That is, replacing the frequency-dependent soil impedance functions by a single-valued functions read at the flexible-base structure frequency; This work seeks to quantify the accuracy of this simplification considering fully coupled two-dimensional (2D) finite element models (FEM) as the reference. Using a Bayesian approach based on ensemble Kalman inversion (EnKI) and a range of numerical simulations of soil–foundation–building interaction, we estimate the optimal frequency that can be used to estimate soil impedance for time domain analyses; and we evaluate the improvement that the corresponding impedance offers relative to the full FEM results when compared to time domain analyses performed in accordance to the NIST recommendations outlined above.
Highlights
Accurate quantification of dynamic soil–structure interaction (SSI) effects is critical in the design of earthquake-resistant structures
In the rest of this manuscript, we provide details of the approach we used to assess the performance of National Institute of Standards and Technology (NIST) recommendations for time domain modeling of SSI effects for two-dimensional (2D) building structures embedded in elastic half-space
Motivated by the inconsistencies that we demonstrated in the NIST definition of the most representative frequency to evaluate single valued stiffness and damping coefficients, we used the ensemble Kalman inversion (EnKI) algorithm to estimate the frequency at which one should read the numerically computed ‘‘true’’ impedance functions to determine the spring and dashpot values in the EnKI-foundation input motion (FIM) reduced order model (ROM)
Summary
Accurate quantification of dynamic soil–structure interaction (SSI) effects is critical in the design of earthquake-resistant structures. Using the NIST and results of soil impedance obtained using EnKI-FIM, we computed the period elongation ratio T~=T and foundation-damping bf that the ROM experiences when supported on lumped spring and dashpot elements (compared to fixed base conditions). Since the proposed ROM considers approximately the coupling between the translational and rotational degrees of freedoms, we employ Equations 31 and 37 derived in Appendix 1 to estimate the period lengthening and foundation damping We compare these results against the iterative method summarized in the ‘‘Introduction’’ section. Motivated by the inconsistencies that we demonstrated in the NIST definition of the most representative frequency to evaluate single valued stiffness and damping coefficients, we used the EnKI algorithm to estimate the frequency at which one should read the numerically computed ‘‘true’’ impedance functions to determine the spring and dashpot values in the EnKI-FIM ROM. Future work by the authors will focus on learning a parameterized functional form that can incorporate the characteristics of the structure, foundation and shaking frequency in the iterative approach of evaluating the global dynamic parameters of building structures accounting for SSI effects
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