Nonlinear seismic wave effects caused by high-energy earthquakes in heterogeneous stratified basins: A refined 2D model of the Aterno Valley in L’Aquila

Abstract

This research extends a previous investigation initiated by the authors focusing on the impact of geometric nonlinearity on the propagation of seismic waves in a two-dimensional model of the Aterno Valley, which includes the urban region of L’Aquila. Starting from a Cauchy continuum framework, this study undertakes a comparative analysis between a traditional linearized formulation, based on infinitesimal strain energy, and a nonlinear model that incorporates the Green–Lagrange strain tensor. The computational domain describes a detailed geological cross-section of the valley, comprising three primary stratigraphic layers. In addition, the upper layer incorporates mechanical segmentation. Furthermore, the excitation is represented as a spherical wavefront applied at the basal boundary, emulating a deep, high-energy source equivalent to an earthquake with a magnitude of Mw ≥ 6. Finite element simulations were performed in COMSOL using a generalized-α time integration scheme. An examination was conducted on two distinct configurations of Young’s modulus distribution within the upper stratum. The first configuration comprised a homogeneous rigid top layer characterized by a unicum body, while the second configuration incorporated soft inclusions within the upper layer to emulate its fragmentation. A comparative analysis was conducted on nonlinear and linear simulations using normalized energy deviation parameters. This approach facilitated the quantification of the relative discrepancies between the deformation energy densities exhibited by the two models. The results indicate that, while the average deviations between the linear and nonlinear formulations are generally moderate, substantial local discrepancies are observed in regions near interfaces with pronounced stiffness contrasts. Specifically, energy deviations in these areas can exceed 100% in certain regions. The observed localized amplifications and redistributions of energy indicate that geometric nonlinearities might significantly affect the spatial distribution of wave energy propagation. This effect is particularly pronounced in scenarios where the shallow layers are mechanically segmented or incorporate compliant inclusions. The temporal evolution of energy at specific reference points within the urban area exhibits scenario-dependent variations, suggesting that linear assumptions may inaccurately characterize site response under conditions of high-intensity excitation. The results confirm the assumption that geometric nonlinearities are significant factors in strongly heterogeneous basins. This emphasizes the need for precise geometric representation and realistic modeling of stiffness distributions to improve predictive accuracy and reliability.