New artificial boundary condition for saturated soil foundations

Abstract

A new artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic analysis. Since shear waves (S-waves) are the same in a saturated soil foundation and a single-phase medium foundation, a tangential visco-elastic boundary condition for a single-phase medium foundation can also be used for saturated soil foundations. Thus, the purpose of the artificial boundary proposed in this paper is primarily to absorb two types of P-waves in a saturated soil foundation. The main idea is that the stress of the P-waves in the saturated soil foundation is decomposed into two types. The first type of stress, σra, is absorbed by the first artificial boundary. The second type of stress, σrb, is balanced by the stress generated by the second artificial boundary. Ultimately, both types of P-waves (fast-P-waves and slow-P-waves) are absorbed by the artificial boundary model proposed in this paper. In particular, note that the fast-P-waves and slow-P-waves are absorbed at the position of the first boundary. Thus, the artificial boundary model proposed herein can simultaneously absorb P-fast waves, P-slow waves and shear waves. Finally, a numerical example is given to examine the proposed artificial boundary model, and the results show that it is very accurate.