Input Seismic Motion Based on the Viscous-Spring Boundary: Analytical Solution and Numerical Simulation

Abstract

Practical geotechnical engineering problems are usually solved within an infinite half-space domain, and a finite domain is necessary to analyze the dynamic response of the medium by the finite element method (FEM). How to deal with the boundary is vital for obtaining accurate results in numerical simulation. This study obtains the analytical solution of input stress at the boundary based on the viscous-spring boundary and develops a procedure for the two-dimensional artificial viscous-spring boundary application in the seismic analysis. The analytical solution based on the viscous-spring boundary is verified using other three artificial boundaries. Furthermore, the simulation accuracy of the procedure is carried out by establishing a two-dimensional model for different element sizes and modified coefficients. The results show that the element size must be in a certain range to avoid the loss of main frequency of seismic motions. When the modified coefficient is less than the suggested value, obvious shifts appear on the calculation results. On the opposite, when the modified coefficient is greater than that, the result will fluctuate dramatically before convergence. All the above factors can lead to a distortion of simulation accuracy of artificial boundary model. Compared with the viscous boundary, viscous-spring boundary has higher simulation accuracy.