The Shah and Heaviside step functions are used to describe the dynamic excitation of the vibratory roller

and the dynamic response analysis of the double-layer foundation with the upper layer of unsaturated soil and the lower layer of saturated soil is carried out. The three-dimensional Fourier transform is used to solve the dynamic control equations of saturated and unsaturated soils

and the dynamic response solution of the double-layer foundation in the transform domain is derived. Through the analysis of numerical examples

the dynamic response of the double-layer foundation under the action of the vibratory roller and the influence of parameters are studied. The results show that the vibration peak value of the foundation will increase accordingly as the excitation frequency and nominal amplitude of the roller increase. When the speed of the road roller exceeds 5 km/h

the vibration peak value of the foundation gradually increases accompanied by fluctuation. The amplitude of the fluctuation depends on the excitation frequency of the road roller. In addition

this paper also considers the influence of saturation on soil shear modulus and permeability coefficient. The study also found that the soil has greater dynamic stiffness and the vibration displacement of the foundation decreases when the saturation is in the range of Sw0~1-Sw0.