Transformation of the Equivalent Linear Method for solving soil-structure interaction problems in the time domain

In the context of soil-structure interaction, often underestimated in design codes, accurate anticipation of dynamic amplification and foundation displacements has become increasingly crucial. Recent earthquakes like Mexico City (1985), Loma Prieta (1989), Port-au-Prince (2010), and Kumamoto (2016) highlighted the need for robust methods to analyze these complex nonlinearities. While both nonlinear and equivalent linear approaches offer valuable insights, limitations in computational efficiency and implementation can hinder their practical application. This paper addresses these challenges by presenting the formal development of a novel quasi-nonlinear method for real-time seismic response analysis, building upon the principles introduced by the author. This innovative approach, unlike traditional equivalent linear methods, dynamically calculates mean shear moduli and local secant stiffnesses, integrating them into a Newmark-based solution process. The paper further validates the method against the Santa Cruz earthquake (Loma Prieta 1989) on a sandy soil profile, demonstrating remarkable agreement with reference solutions obtained using established methods like Shake91 and Quad4m. This comprehensive formulation paves the way for accurate and efficient real-time reconstruction of seismic responses within a practical quasi-nonlinear framework.