When a strong ground motion strikes a slope, it is expected that a one-sided residual displacement will take place. We proposed a one-sided bilinear single-degree-of-freedom (OSB-SDF) model to reproduce the one-sided residual displacement in the slope. The values of the defining parameters for the OSB-SDF model must be determined to match the characteristics of the slope. First, we performed a two-dimensional nonlinear finite element (FE) analysis on an example slope. Second, we determined the parameters of the OSB-SDF model that could reproduce this time-history response of the slope top using Particle Swarm Optimization (PSO). A single cycle of a sinusoidal wave was input horizontally. The amplitude of the input wave was set to two cases (4.0 and 8.0 m/s/s), and the frequency varied in 0.2 Hz increments from 0.2 Hz to 4.6 Hz. The natural period in the elastic range was set to 0.49 s, which is the first mode eigenvalue obtained from the FE model. The other parameters were determined using PSO. 
The displacement responses at the slope top obtained from the finite element model were compared with the displacement responses calculated using the OSB-SDF model. Although the two show very good agreement, the OSB-SDF model parameters vary with the amplitude and period of the input motion.