Bayesian Hybrid-Surrogate Modeling of Dynamic Soil–Foundation–Structure Interaction A Multiscale Formulation for Coupled Nonlinear Systems

Dynamic soil–structure interaction (SSI) is a coupled boundary-value problem inwhich foundation motion and structural response depend on the deformability, inertia,damping, and nonlinear constitutive behavior of the supporting ground. A fixed-baseapproximation can therefore misrepresent natural periods, damping, foundationrotation, and seismic demand, particularly when soil or structural response isnonlinear. This paper presents a physics-informed framework combining continuummechanics, frequency-dependent foundation impedance, finite-element modeling,Bayesian parameter inference, and hybrid surrogate models. The coupled equationsare stated in time and frequency domains. Soil nonlinearity is represented throughconstitutive relations, while radiation effects are represented through impedanceoperators or absorbing boundaries. A Bayesian workflow is formulated to updateuncertain soil and interface parameters from field, laboratory, or structural-responseobservations. The proposed surrogate combines a mechanistic baseline with a learned discrepancy term, preserving physical structure while reducing the cost of repeatednonlinear simulations. Verification, validation, and application procedures are alsodescribed. This manuscript is a theoretical and methodological synthesis; it doesnot report new experiments or claim validation for a particular site or structure.