Seismic actions are usually considered for their inertial effects on the built environment. However, additional effects may be caused by the volumetric-distortional coupling of soil behaviour: the fast cyclic shaking on saturated soils caused by earthquakes generates temporary undrained or quasi-undrained conditions and subsequent pore pressure variations that, if positive, reduce the effective stresses, eventually leading loose granular soils to liquefaction. Whatever the amount of seismically induced pore pressure build up, buildings on shallow foundations suffer settlements and tilts that may be extremely large when soils approach liquefaction, as demonstrated by several recent case histories. The paper proposes an equivalent elastic approach in effective stresses to predict the co-seismic (undrained) component of the seismically induced settlement of shallow foundations, which usually is the most relevant one, by considering the decrease of soil stiffness during the seismic event. The total settlement can be then estimated by adding the post-seismic (drained) component, also evaluated in this paper via a quite simple approach. Even though the equivalent elastic model is stretched into a highly non-linear soil behaviour range, especially when the soil is approaching liquefaction, the model considers the relevant capacity and demand factors and proved effective in simulating some centrifuge tests published in the literature. In the paper, the simplifying assumptions of the approach are clearly indicated, and their relevance discussed. It is argued that notwithstanding some limitations the model is physically based and therefore it allows for understanding and checking the relative relevance of all the parameters related to soil, foundation, and seismic action. Thus, it is a tool of possible interest in the design of shallow foundations in liquefaction-prone seismic areas.

This paper presents the findings of a series of shaking table tests conducted to investigate the seismic damage and dynamic characteristics of a tunnel crossing a sliding surface system. An evaluation methodology is introduced to assess the model's boundary effects and dynamic characteristics. In this study, we propose a model soil failure mode assessment method based on Marginal Spectral Entropy (MSE) using Hilbert-Huang Transform (HHT) and information entropy parameters. Furthermore, a damage evaluation method for tunnel lining is presented, which utilizes the Hilbert Energy Spectrum (HES) and an Empirical Mode Decomposition (EMD) energy damage index. The results of the tests reveal that the MSE accurately reflects the slope failure process and provides insights into the depth of the sliding surface. The observed behavior of the model indicates a push-back shear slip type characterized by sinking, squeezing, pulling, and shearing. The HES analysis of the model soil indicates that the energy primarily concentrates in the frequency range of 0 to 25 Hz, expanding with elevation. Notably, the tunnel crossing the hauling sliding surface exhibits a more pronounced broadband effect in the model soil compared to the main sliding surface. The peak HES of the lining occurs after that of the model soil and is found to be 18.07 s. The damage index distribution correlates with the spatial position of the lining parts. When the damage index exceeds 90 %, it indicates the presence of significant damage to the specific parts of the lining, a finding that has been validated through post-seismic analysis. Furthermore, the EMD energy damage index, in conjunction with dynamic finite element simulation, demonstrates its potential for preliminarily determining the location and extent of lining damage through abrupt changes. The research findings contribute to the theoretical understanding of extracting damage features in tunnel-landslide models.