Inerter-enhanced trench-based seismic metamaterial in soils with multiple impedance contrasts for seismic wave diversion and attenuation

• Novel inerter-based seismic metamaterial for frequencies as low as 1 Hz. • Local resonancemechanismwithout relying on discrete heavy embedded resonatormasses. • Applicable to multi-layered soil with high impedance contrast. • Up to 80% reduction in acceleration amplitudes. • Ground above inerter-based seismic metamaterial remains usable. While seismic metamaterials have been widely studied in homogeneous soil half-spaces and increasingly in layered media, the influence of multiple, deep impedance contrasts typical of realistic geotechnical site profiles on low-frequency surface wave attenuation remains incompletely quantified. Simplified soil representations may overestimate attenuation effectiveness and underestimate the required barrier length for low-frequency applications. This study examines the influence of multiple impedance contrasts in a deep soil profile on the performance of seismic metamaterials in attenuating low-frequency seismic surface waves. A novel inerter-enhanced trench-based seismic metamaterial is proposed, consisting of periodic concrete trenches in which the confined soil acts as an effective dynamic mass coupled to inerters. The design exploits both Bragg’s scattering effects and local resonance within the trench-soil system, enabling effective attenuation of surface waves at frequencies as low as approximately 1 Hz without the use of discrete heavy embedded masses or excessively deep trenches. The trenches incorporate concrete walls to stabilise the soil and improve constructability, while the inerter provides tunable apparent inertia that reduces the natural frequency of the trench-soil system. Using finite element analysis in both frequency and time domains, and a soil profile from Christchurch Central Business District, New Zealand, the study demonstrates the ability of proposed configuration to protect buildings from seismic waves in areas with shallow, medium, and deep soil profiles. Overall, this study establishes the first demonstration of an inerter-enhanced trench-based seismic metamaterial in a realistic multi-layered soil with multiple impedance contrasts, providing practical pathways for implementation.