A supervised approach for improving the dimensionless frequency estimation for time-domain simulations of building structures on embedded foundations

The analysis of soil-structure interaction (SSI) problems has been established successfully in recent decades. In particular, the solution in the frequency domain provides an exact and efficient method for computing the response of the coupled system. Despite this, the state of practice as a first attempt to incentivize time domain analyses compatible with standard finite element packages introduces the so-called dimensionless flexible-base frequency. This frequency, which depends solely on the structure-to-soil-period ratio, allows transforming the frequency domain analyses into time domain analyses using frequency-independent soil impedance values. However, if such frequency exists for the combined system, it must depend on several physical variables. In this work, we propose a supervised approach to obtain the flexible-base dimensionless frequency at which the frequency-independent soil impedance should be used. The analysis is carried out using five dimensionless parameters, and the importance of each one to the estimation of the dimensionless flexible-base frequency is investigated. We use an inverse problem based on ensemble Kalman inversion (EnKI) to obtain the optimal frequency of the interaction. The data obtained are then employed in a machine-learning framework to map a set of dimensionless parameters to such a frequency. The generated mapping is finally verified, and a significant improvement in time-domain simulations is shown compared to the state of practice.