A TIME-DOMAIN ARTIFICIAL BOUNDARY CONDITION FOR VECTOR WAVE IN MULTILAYERED WAVEGUIDE

A time-domain artificial boundary condition (ABC) is proposed to simulate the in-plane vector wave in a linear elastic multilayered waveguide with Rayleigh damping. The ABC is stable and can be seamlessly coupled with the finite element method. First, the vector wave equations of the multilayered waveguide are simplified to two scalar wave equations, which are decoupled in both x and y directions. Then, based on the scaled boundary finite element method, semi-discrete frequency-domain dynamic stiffness in the modal space is obtained. The dynamic stiffness can be approximately expressed as matrix continued fraction. Finally, the continued fraction is converted to the time-domain ABC by introducing the auxiliary variable technique. In this method, the parameters affecting the calculation accuracy and efficiency include the mode number n, the order J of continued fraction, and the distance L from the artificial boundary to the region of interest. Numerical examples show that only the mode numbers of the infinite domain excited by the load have to be used. J=3 can be taken generally. The value of L is independent of the size of the underground structure. But it is proportional to the total height H of the soil layer, and the relation coefficient is related to the material parameters of the soil layer.