Analytical and finite element investigation of SH-type wave behavior in a reinforced layered stratum with stress discontinuities

Abstract

This study develops a theoretical model consisting of a fiber-reinforced elastic layer overlying a homogeneous half-space to analyze the influence of shear stress discontinuities on free-surface motion. Analytical solutions for the displacement field are derived using the Laplace transform method in combination with the generalized Cagniard-de Hoop technique. The influence of three distinct types of stress discontinuities on free-surface dynamics is examined. Numerical computations of the displacement components are carried out using the Finite Element Method (FEM), and the results are validated against the analytical solutions to confirm the accuracy of the proposed model. A comprehensive analysis of convergence behavior and stability is performed under various material properties and fiber orientation configurations. The numerical simulations, implemented in MATLAB, successfully capture wave attenuation, phase variations, and the influence of material anisotropy, thereby demonstrating the robustness and reliability of the proposed FEM framework for analyzing complex layered media. The graphical results indicate that shear stress discontinuities produce non-uniform and impulsive behavior in SH-type waves, with the intensity and persistence of jerks depending on the reinforcement parameters. These discontinuities are associated with the initiation and propagation of fractures, as commonly observed during seismic events such as earthquakes and underground explosions. The proposed model offers potential applications for seismologists and civil engineers in estimating ground-surface displacement and enhancing the understanding of wave dynamics in anisotropic, reinforced media. Validation through comparison with previous studies further confirms the reliability and accuracy of the present model. © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2025.