Equivalent linearization in frequency domain

represented by SHAKE2000

is the mainstream approach for seismic response analysis of soil layers. Due to the severe unreasonable results in soft soil sites

its improvement becomes a research hotspot

which mainly adopts frequency-dependent method (FDM)

but there has been no substantial improvement. This paper assumes that dynamic shear strain and vibration velocity present a constant proportional relationship in FDM. Based on wave equation

exact solutions for the relationship of the two variables were derived on three typical site models

i.e.

the homogeneous half space with one-way traveling wave

the single uniform soil layer

and the layered soil site. The reasonability and deviation degree of the assumption were studied through numerical experiments. Results show that the constant proportional hypothesis only applies in the case of unbounded homogeneous medium with one-way traveling wave. For actual layered soil sites

the relationship between dynamic shear strain and vibration velocity strongly depends on the frequency of the wave and the location of the observation point. If we ignore the reflection wave in ground seismic response analysis

the use of constant proportion assumption under one-way traveling wave will make significant deviation to the results. The deviation caused by the assumption may span four orders of magnitude. Even for a single uniform deposit

the deviation is also very significant. For practical ground motion calculation

this assumption clearly exists qualitative error in theory

and the quantitative deviation can not be acceptable

so it must be abandoned and need to find another more reasonable approach.