An efficient finite element framework for nonlinear seismic soil-foundation-structure interaction in shallow-founded squat masonry structures

Fully nonlinear three-dimensional simulations of masonry structures with realistic soil–foundation-structure interaction (SFSI) remain computationally demanding, particularly when capturing material nonlinearity and interface behavior under long-duration seismic excitations. This study presents an OpenSees-based finite element framework that integrates nonlinear masonry, interface, soil-plasticity, coupling, and boundary formulations in a direct SFSI model. The mixed implicit-explicit (IMPL-EX) material-integration strategy is used for the masonry and contact/interface model to improve numerical tractability in large nonlinear dynamic simulations. The proposed framework is applied to a representative historical masonry tower on fine-grained saturated soil, indicating an interaction mechanism: cracking damage in the foundation masonry results in reduced lateral confinement on the underlying soil. This leads to amplified nonlinear shear distortions, and eventually larger ratcheting settlement accumulation. The response is consistent with rocking isolation observed in reinforced concrete structures, and, in this study, it is studied in the context of historical masonry towers. The results indicate that the rate of soil shear-modulus degradation strongly influences the structural response: steeper degradation limits high-frequency energy transmission, reducing masonry damage at the cost of increased settlement. Comparisons with fixed-base and linear-soil models suggest that neglecting foundation flexibility in the analyzed tower can overestimate seismic demand, whereas neglecting cracking in the foundation masonry can underestimate ratcheting settlement. The residual foundation rotations remain within the adopted serviceability threshold, highlighting a possible trade-off between reduced seismic demand and increased residual foundation deformation. Computational comparisons show that the IMPL-EX formulation reduces solution time relative to fully implicit integration while preserving the relevant global response metrics for the analyzed case.