Theoretical solution to the isolation effect of periodic structure wave impeding block in layered transverse isotropy soil

Periodic structure wave impeding block (PSWIB) has bandgap characteristics compared to traditional wave impeding block (WIB). The composition parameters of PSWIB can be designed based on the characteristics of the vibration source to achieve isolation of the target frequency vibration. However, existing research has overlooked the interaction between PSWIB and the surrounding soil. Therefore, this study considers the site around PSWIB as a layered transversely isotropic (TI) soil. Based on the theory of phononic crystals and equivalent media, the stiffness matrix method is used to derive the basic solution of the dynamic response of PSWIB in layered TI sites, and to evaluate the vibration isolation performance of PSWIB in soil media. Theoretical analysis shows that compared with traditional WIB, the isolation efficiency of PSWIB is improved by about 43.3%. The geometric parameters such as the number of cycles and the number of cycles per layer have a positive regulatory effect on the isolation effect, while the influence of burial depth reaches its peak at <italic>t</italic>=0.8<italic>B</italic>, and the acceleration amplitude decreases by 1.17m/s^-2. In addition, TI characteristics and the incident angle of the wave significantly affect the dynamic response of the site. When <italic>Eh/Ev</italic> increases from 0.5 to 2.0, the peak displacement increases by 17.5%, corresponding to a decrease in dominant frequency.