Isolation effect of periodic wave impeding block in layered transversely isotropic soil

Wave impeding blocks (WIB) are often used as a wave barrier for vibration control. However, its isolation range is limited by the soil cut-off frequency, which limits practical effectiveness. Therefore, this study original proposes a periodic structure wave impeding blocks (PSWIB) and derives an analytical solution for the dynamic response of PSWIB in a layered transversely isotropic (TI) soil. The band gap theoretical model of PSWIB was established using the plane wave expansion method, and the band gap results were solved using MATLAB. Subsequently, based on the phononic crystal theory and the effective medium theory, the stiffness matrix of the PSWIB was solved, and the fundamental solution of the vibration isolation effect of PSWIB in a layered soil was derived using the stiffness matrix method. Theoretical analysis indicates that PSWIB outperforms traditional WIB in vibration isolation performance. Reducing the period constant, increasing the elastic modulus ratio of the cladding layer, and increasing the density of the filling material can effectively expand the bandgap. Compared to isotropic soil, the TI characteristics of soil significantly affect its dynamic properties, resulting in notable changes in displacement peaks and peak frequencies. Finally, the calculation results show that, in layered TI soil, altering the burial depth, the number of layers, and the number of periods can enhance the vibration isolation performance of PSWIB. Overall, PSWIB breaks through the constraint of soil cutoff frequency and realizes the isolation of target frequency vibration by designing its composition parameters based on the characteristics of the vibration source.