Seismic surface wave mitigation using metamaterials is a growing research field propelled by intrinsic theoretical value and possible application prospects. Up to date, the complexity of site conditions found in engineering practice, which can include layered stratigraphy and variable water table level, has been discarded in the development of analytical frameworks to favor the derivation of simple, yet effective, closed-form dispersion laws. This work provides a further step towards the analytical study of “seismic metasurfaces” in real site conditions considering the propagation of Rayleigh waves through a layered porous substrate equipped with local resonators. To this aim, we combine classical elasticity theory, Biot’s poroelasticity and an effective medium approach to describe the metasurface dynamics and its coupling with the poroelastic substrate. The developed framework naturally includes simpler configurations like seismic metasurfaces atop homogeneous dry or saturated soils. Apart from known phenomena like wave-resonance hybridization and surface wave band gaps, we predict the existence of an extended frequency range where surface waves are attenuated due to energy leakage in the form of slow pressure waves, as a result of the fluid-solid interaction. Besides, we demonstrate that the surface wave band gap and the related surface-to-shear wave conversion is robust to variations in the water table level. Conversely, when the dry and saturated layers have different material parameters, for example, due to different porosity ratios, the surface-to-shear wave conversion can be accompanied by the excitation of higher-order surface modes, which remain channeled below the metasurface. These analytical findings, augmented and confirmed by numerical simulations, evidence the importance of accounting for fluid-solid interaction in the dynamics of seismic metasurfaces.

利用固有材料减轻地震表面波是一个不断发展的研究领域，其固有的理论价值和可能的应用前景推动了该领域的发展。迄今为止，在工程实践中发现的复杂的现场条件（包括分层的地层和可变的地下水位）已在分析框架的开发中被抛弃，以利于推导简单而有效的封闭形式的扩散规律。考虑到瑞利波通过装有局部谐振器的层状多孔基底的传播，这项工作为实地条件下的“地震超表面”的分析研究提供了进一步的步骤。为此，我们结合了经典弹性理论，Biot的多孔弹性和一种描述超表面动力学及其与多孔弹性基底耦合的有效介质方法。发达的框架自然包括更简单的配置，例如在均质的干燥或饱和土壤上的地震超表面。除了诸如波共振杂交和表面波带隙之类的已知现象外，我们预测还会存在扩展的频率范围，在该频率范围内，由于流固相互作用，能量以慢压力波的形式由于能量泄漏而衰减。 。此外，我们证明表面波带隙和相关的表面到剪切波转换对于地下水位变化具有鲁棒性。相反，当干燥层和饱和层的材料参数不同时（例如，由于孔隙率不同），从表面到剪切波的转换可能伴随着高阶表面模态的激发，这些模态保持在超颖表面之下。这些分析结果得到了数值模拟的增强和证实，证明了在地震超地表动力学中考虑流固耦合的重要性。