# Seismic Isolation via I-Shaped and T-Shaped Large-Scale Phononic Metamaterials
## 4 Discussion and Conclusions
The results, although expected to exhibit some differences with the corresponding ones of the band structure, nevertheless are in very good agreement with the latter, validating thus the predictions based on the calculations of the dispersion relations. Therefore, the extracted conclusions from the dispersion relations for all the examined geometries are safe and indicate that each of the proposed geometries could be a potential candidate for applications in seismic isolation. It should also be noted that a reduction in the lattice constant of the structure ten times would cause a shift in the limits of the PBGs ten times to higher frequencies. In more detail, for lattice constant \(\alpha=1\) m, the geometric dimensions of the I-shaped trench would have been \(\mathrm{L}=0.9\) m and \(\mathrm{w}=0.4\) m. Relevantly, the two calculated PBGs would have been calculated between 16.8 and 31.0 Hz and between 32.6 and 37.4 Hz. Considering that the geometric dimensions of the I-shaped trench for \(\alpha=1\) m are of the same order of magnitude with a relevant structure that has already been experimentally verified in [23] (for which the lattice constant was 1.73 m and the diameter of the holes was 0.32 m), the calculated PBGs for \(\alpha=1\) m are also in the same order of magnitude with [23], thus indicating that the calculated results of this study are reasonable for the examined dimensions and soil selection. The proposed structures are easy to fabricate; they do not interfere with an existing structure and provide PBGs that are in the very low frequency range of the phononic spectrum, thus achieving the attenuation of surface waves of vibrations caused at these wavelengths. All studied structures provided wide PBGs within a frequency range less than 6 Hz. The selected lattice constant, although it could raise some construction difficulties, especially for the case of the steel-coated core, is mandatory for the formation of PBGs in the very low frequency range. Moreover, better comparison between the studied structures can be achieved by the selection of the same lattice constant. It should also be noted at this point that stability issues, which could arise by the selection of the sandy type of soil for the cases of I-shaped or T-shaped LSPMs, could be easily addressed by the addition of a thin layer of a stiff material that can hold the sandy soil. Although this addition could cause a slight shift in the PBG limits to higher frequencies, this shift is not expected to modify the attenuation performance of the structures. In addition, the PBGs of the structures could also be retained in the same range despite the addition of a thin layer of stiff material by selecting a bit higher lattice constant \(\alpha\). The present contribution included a holistic numerical approach of a novel group of structures that can have a significant number of applications when surface wave attenuation is needed. This study, although focused on applications that include isolations from seismic surface waves, provided a compact and representative content suitable for other possible applications when considering other values of \(\alpha\). Taking into account that the investigation towards new and easy-to-fabricate schemes for seismic isolation is of constant demand, the present work responded to this call and enriched the field by proposing a group of large-scale phononic metamaterials as possible candidates for protecting existing or future buildings and structures. All authors contributed equally to this work. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Not applicable. Not applicable. Not applicable. Data Availability Statement: The raw data supporting the conclusions of this article will be made available by the authors on request. The authors declare no conflicts of interest.