Sheer particle system method only the material damping of soil can be taken into account

while the radiation damping can’t be taken into account

that exaggeratedly estimates the seismic response of layered foundation. This paper improved the sheer particle system by replacing the fix boundary by a viscous boundary

using Rayleigh damping model to consider the soil damping and using Wilson-theta method to accelerate calculation speed. The improved sheer mass particle method can consider the radiation damping and material damping at the same time in seismic response analysis which is more comprehensive. This improvements is proved to be effective by comparing the calculated result with the imaginary layered foundation. The comparative analysis indicates that the maximum displacement of foundation surface considering the material damping and radiation damping at the same time is about 25% and 35% smaller than only considering one type of damping.