A novel insight into vertical ground motion modelling in earthquake engineering

Recent observations of failure and damage of buildings and structures under seismic action has led to an increasing interest for an in-depth analysis of the vertical component of site ground motion. In particular, when dealing with saturated soils, the current engineering practice does not usually go beyond the simplified u-p formulation of the Biot's equations describing the coupled hydro-mechanical behaviour, thus neglecting some terms of fluid inertial forces, despite the presence of more refined formulations, for example, the u-U formulation. Therefore, a theoretical and numerical validation of the u-p formulation as compared with the u-U formulation is proposed in this work, where the numerical simulations are compared with the analytical solution for the u-p formulation, which is also derived and illustrated in this text. The comparison between the two formulations and the analytical solution is provided for different levels of permeability and dynamic actions, which are representative of a wide scenario of site ground properties and seismic hazard in the vertical direction. In particular, the soil response is analysed in terms of acceleration and pore pressure time history, frequency content, acceleration response spectrum, and amplification ratio of acceleration. This study extends the discussion of the limits of applicability of the u-p formulation with respect to the rigorous solution of Biot's equations (obtained here with u-U formulation) to the context of a complex dynamic regime provided by the vertical components of real earthquake records, and paves the way for further investigations.