Metasurfaces provide a promising solution for modulating low-frequency surface waves (SW) in sub-wavelength size. However, they were coupled with single-phase soil or saturated soil in previous investigations, rather than the more common unsaturated soil whose properties cannot be simply evaluated from single-phase and saturated soils. Otherwise, they would not be operational in the intended frequency range. In addition, the screening performance of metasurfaces in unsaturated soils is unknown to us due to the complex physical fields and constitutive relationships of unsaturated soils. In this work, an analytical formulation is proposed to investigate interactions between SW and an array of resonators located atop the free surface of unsaturated soil semi-space and to evaluate the vibration damping performance of the metasurface in single-phase, saturated and unsaturated soils. The incident and scattered wave fields are clearly captured by using the Green's functions of an unsaturated semi-space subjected to a harmonic excitation source. Based on the multiple scattering theory, the displacement of the total wave field as well as some complex phenomena (surface-to-bulk wave conversion) are obtained and also validated in a 2D finite element model. It is notable that incorporating a resonator with different natural frequency create a new bandgap, implying that we can broaden the bandgap by installing more resonators with different natural frequencies. We expect this analytical formulation could solve SW scattering problems in geotechnical engineering, and the system with a broad bandgap could provide a conceptual design for weakening SWs.

中文翻译：

---

超表面在非饱和土中的表面波调控：理论研究


超表面为调制亚波长大小的低频表面波 （SW） 提供了一种有前途的解决方案。然而，在以前的研究中，它们与单相土壤或饱和土壤耦合，而不是更常见的非饱和土壤，其特性不能简单地从单相和饱和土壤中评估。否则，它们将无法在预期的频率范围内运行。此外，由于非饱和土具有复杂的物理场和本构关系，我们不知道超表面在非饱和土中的筛选性能。在这项工作中，提出了一种解析公式来研究 SW 与位于非饱和土半空间自由表面顶部的一系列谐振器之间的相互作用，并评估超表面在单相、饱和和非饱和土壤中的减振性能。通过使用受谐波激发源影响的不饱和半空间的格林函数，可以清楚地捕获入射波场和散射波场。基于多重散射理论，获得了总波场的位移以及一些复杂的现象（表面到体波的转换），并在二维有限元模型中进行了验证。值得注意的是，加入具有不同固有频率的谐振器会产生新的带隙，这意味着我们可以通过安装更多具有不同固有频率的谐振器来扩大带隙。我们期望这种分析公式可以解决岩土工程中的 SW 散射问题，并且具有宽带隙的系统可以为弱化 SW 提供概念设计。