Equivalent Linear Analysis of Semi-Infinite Free-Field Column Using PML

One of the important factors in determining the response of the structures is the correct evaluation of the input motion. This input excitation can be affected by various factors such as the propagation of waves in different layers, site effects, interaction of soil-structure, etc. Another problem with the numerical analysis is the use of appropriate absorbing boundaries to prevent the return of scattered waves into the analysis environment. Besides, the non-linear behavior of construction materials can also change the propagated waves, which makes the problem more complicated. One of the simple methods to estimate the nonlinear behavior of materials is to use the equivalent linear analysis method, which is still used due to its simplicity and ease of use. In this research, by preparing the finite element time domain dynamic analysis code using C programming language, the response of the free field, which is the first step in estimating the soil-structure interaction effect, has been evaluated using the equivalent linear analysis method. In addition, to increase the accuracy of the results, radiation damping simulation by perfectly matched layers (PML) has been implemented. This program uses four-nodded quadrilateral elements and the implicit Newmark method to solve the dynamic equation. For using PML in the equivalent linear method, the PML properties were updated based on adjacent elements to avoid reflection from boundaries. The results showed that the nonlinear behavior of materials can change responses significantly in a way that it be far away from results of the linear analysis. Furthermore, the results showed that the procedure adopted to perform equivalent linear analysis using PML is efficient.