The influence of stratigraphic conditions in horizontally layered soils on the propagation dynamics of seismic waves

The viscous-spring artificial boundary, recognized as an efficacious approach for assessing ground motion, finds widespread application in finite element analysis. When using this method to analyze the oblique incidence of seismic waves in horizontally layered soils, there are difficulties in accurately calculating the time delay. To solve this, a new method for calculating the time delay is proposed, which is based on the virtual starting point of seismic waves. This method includes tracing and iterating the wave path to determine the virtual starting point. Once it is determined, the time delay of the target point can be solved according to the current wave velocity. On this basis, by using the Snell equation and the continuity condition of seismic ground motion at the sub-layer interface, the equation for equivalent nodal force is derived, thus establishing a method for simulating the oblique incidence of seismic waves in horizontally layered soils. The proposed method standardizes the form of the equation, including only the parametric characteristics of the soil layers, which makes the calculation easier. To validate the accuracy of this approach, a three-dimensional finite element model was built. This model was used to study the variation patterns of ground displacement caused by ground motion under different stratigraphic conditions. The root causes were analyzed to provide insights and guidance for engineering seismic research.