Engineering low-frequency vibration attenuation in soil with multilayer phononic pile barriers

In this work, we investigate the attenuation of low-frequency vibrations using two-dimensional phononic pile barriers formed by periodic cylindrical inclusions embedded in sandy soil, targeting the propagation of elastic waves in the 1–100 Hz range, relevant to civil engineering structures. Numerical calculations, based on the finite-element method, are used to analyze dispersion relations and bandgap behavior in square and triangular lattices. Single, bilayer, and trilayer piles combining concrete, steel, and rubber are considered. The results show that triangular lattices systematically produce wider and more continuous bandgaps as a result of their increased packing density, while material layering enables cutoff frequencies to be tuned through impedance contrast and elastic-compliance effects. This work provides an extensive parametric mapping of soil-embedded phononic barriers and offers design-oriented guidelines for low-frequency vibration mitigation systems based on realistic materials. Significant bandgaps are obtained in the ranges of 1–10 Hz, 10–50 Hz, and 50–100 Hz, with potential applications in vibration-sensitive structures, road-traffic mitigation, and construction-induced vibration control, respectively.