Because the foundation is placed on the foundation, the comprehensive stiffness KF of the foundation and foundation can be regarded as the series connection of the foundation stiffness KF1 and the foundation stiffness KF2

The foundation is regarded as an elastic half space with isotropy, Poisson’s ratio V and shear modulus G. The length of the block foundation is 2L, the width is 2B, the buried depth is e, and the height is h, as shown in the figure. The formulas for calculating the vertical stiffness KF1 and the rotational stiffness K θ f around the horizontal axis of the rectangular foundation are given

For the rectangular section block foundation, according to the calculation formula of deformation under tension or pressure f in the mechanics of materials:

The stiffness can be obtained as follows

Here, Δ h is the vertical deformation.

For the calculation of damping, several methods of calculating damping ratio are introduced, one of which is dynamic stiffness method. The expression of dynamic stiffness K is as follows:

The imaginary part kimg is related to damping and is equal to the product of equivalent viscous damping coefficient and excitation frequency. In other words, as long as the value of dynamic stiffness is known, the damping coefficient can be determined. The calculation formula of dynamic stiffness of rectangular foundation considering foundation embedment is given