Effect of initial stress on attenuation zones of layered periodic foundations

• Weak form quadrature element method is introduced to study attenuation zones.
• The proposed method convergence faster than the plane wave expansion method.
• Layered periodic foundations model including the effect of initial stress are proposed.
• The attenuation zones shift to lower frequency range due to compressive initial stress.
• Maximum attenuation coefficient within attenuation zones is independent of initial stress.

Layered periodic foundations have been proposed to isolate seismic waves and support upper structures. Before seismic waves arrive, initial stress exists in the layered periodic foundation due to the load from the upper structures. Based on the weak form quadrature element method, this paper proposes a novel numerical approach to study the effect of initial stress on the attenuation zones of layered periodic foundations. Comparisons with existing results in special cases are conducted to validate the proposed method, and good agreement is found. The theoretical results illustrate that the compressive initial stress shifts the attenuation zones to a lower frequency range. In addition, the maximum attenuation coefficient in each attenuation zone is not affected by the initial stress. Furthermore, frequency-domain and time-domain response analyses of a building with a finite-unit cell layered foundation are conducted. The present work is very helpful for the design and application of periodic foundations in seismic isolation.