Seismic analysis plays a vital role in dam engineering because earthquake-induced loading can trigger instability, deformation, and liquefaction within embankment and tailings structures, leading to potentially sudden and catastrophic failure. While one-dimensional (1D) site response analysis remains widely used due to its simplicity, dam systems inherently exhibit complex two- or three-dimensional behavior. To quantify the influence of 2D wave propagation mechanisms when liquefaction is present, we perform a comparative evaluation of 1D and 2D site response and liquefaction analyses based on a typical dam cross-section in North America. The dam selected in this study is a zoned embankment structure comprising an inclined central clay core, protected by a layer of filter material and rockfill, and a clay cutoff trench designed to control seepage through the foundation. Results including acceleration time histories, pseudo-spectral accelerations, and stress path evolution were discussed in the paper. It was concluded that within the 1D framework, liquefied soil layers significantly limit upward seismic wave propagation due to reduced stiffness, resulting in a dampened seismic response within the embankment. In contrast, the 2D geometry captures additional wave propagation mechanisms associated with 2D dam geometry. The results indicate that, for the dam considered in this study, the presence of a cutoff trench provides a pathway for seismic energy to bypass liquefied foundation zones, contributing to higher site response motions than those predicted by the corresponding 1D analysis. The 1D analysis predicts peak acceleration amplitudes of only approximately 0.06g, whereas the 2D analysis yields peak accelerations of about 0.20g after the onset of liquefaction at the crest. These findings suggest that simplified 1D analyses underestimate site response for the case study examined herein after the onset of the liquefaction. This comparative study highlights the case where 2D modeling provides more insight into the potential seismic response, particularly in capturing internal stress redistribution during liquefaction, localized amplification effects, and more representative deformation mechanisms governed by the behavior of true 2D system.  It should be noted that the quantitative differences reported herein are specific to the representative dam geometry, material properties, and input motion adopted in this study.  However, the objective of this study was not to perform a site-specific seismic hazard assessment or to reproduce the response to a particular design earthquake, but rather to compare the differences between 1D and 2D dynamic analyses when liquefaction is present.  Further parametric studies incorporating a wider range of dam geometries, foundation conditions, and seismic input motions are required to quantitatively assess the differences observed between the 1D and 2D analyses and to evaluate the broader applicability of the findings.