Data-driven approximation of geotechnical dynamics to an equivalent single-degree-of-freedom vibration system based on dynamic mode decomposition

The application of data science technologies in geotechnical and earthquake engineering is a hot topic. This study aimed to identify the macroscopic dynamic properties of the soil from the previous records of seismic motions observed at the ground surface utilizing the dynamic mode decomposition (DMD). The key to our ingenuity was to replace the soil layer composition and dynamic properties with a single-degree-of-freedom (SDOF) vibration model based on the ground surface observation records. In the validation process, first, a comparison was made between the proposed method and the analytical solution for an SDOF vibration system; second, a comparison was made with a one-dimensional equivalent linear multiple reflection theory analysis considering the nonlinear soil profile. The proposed method effectively approximated complex ground profiles to an equivalent SDOF vibration system and constructed shear strain-dependent models of the macroscopic pseudo-shear modulus and damping constant from the observed ground surface seismic motions. This study was based on numerical experiments and limited conditions of small seismic amplitudes for which equivalent linear approximations could be made. Based on the results obtained in this paper, we aim to extend the model to wide-area forecasting by improving it to a practical model that covers strong nonlinearities.