Green function analysis of rocking interaction between soil and adjacent strip foundations

The rocking interaction between adjacent strip foundations is studied based on the elastic half-space theory. The interface between the foundations and the supporting medium is divided into a number of strip elements. Asymmetrical Green function of the displacement of elastic soil medium under harmonic uniform excitation is derived. The multi-value improper integral is precisely calculated by the piecewise integration method and Cauchy principal value integral. The coupling rocking impedances between soil and adjacent strip foundations are solved. The bending moments caused by the contact forces of Green function is added on each element. The analysis uses the fact that the displacement of a rigid foundation determines that of each element. Influences of calculating parameters of foundation and soil medium on the rocking interaction between two foundations are discussed in detail. The numerical results show that the rocking interaction between adjacent strip foundations should be taken into consideration when the spacing and width ratio S/L is less than 4.0. This method is simple, has a highly accurate, and can be used for the calculation at a high frequency range. The research results provide a theoretical basis for the study of soil-foundations dynamic interaction, and make it convenient for engineers to consider dynamic interaction between adjacent foundations in the seismic design of structures.