The TIMg Approach and Its Generalisations: A Unified Thermodynamic Inertial Macroelement Framework for the Multiphysics Response of Soil-Structure Systems

The response of the soil-foundation system can critically impact the dynamic performance of structures. However, its consideration commonly requires ex-haustive numerical modelling, warranted only for cases of major importance. To bridge this methodological gap, the present contribution advances a unified Thermodynamic Inertial Macroelement, TIMg, as an energy-consistent model for the nonlinear analysis of soil-structure systems. The TIMg relates the gen-eralised forces acting on a geotechnical system (whether a shallow/deep foun-dation, or a bridge abutment) and the resulting deformations through a tangent operator formulated within a hyperelastic-hyperplastic framework with com-bined isotropic-kinematic hardening. The model captures translational-rotational modes, frequency dependence and nonlinear features under multiaxi-al static, cyclic and dynamic loading. Recent extensions enable hydro-mechanical coupling in saturated soils, and provide the basis for incorporating interaction among neighbouring footings and thermo-hydro-mechanical soil behaviour. Example applications demonstrate the capability of the framework for performance assessments ranging from local to territorial scale.