The relative density of a granular soil medium has an important influence on its mechanism of shear deformation. Dense soils tend to shear in a brittle manner with distinct localization; whereas, loose soils tend to show broadly distributed deformation with no distinct localization. These general modes of shear deformation also manifest at the field scale as evidenced by case studies of earthquake surface fault rupture. The influence of relative density on earthquake surface fault rupture is important to fully understand because of the devastating effects this hazard can have on the built environment as demonstrated most recently by the 2016 Kaikoura, New Zealand earthquake. The discrete element method (DEM) is a valuable numerical tool for analyzing the influence of relative density on earthquake surface fault rupture propagation because it models directly the grains and pore space within a granular medium. This influence is modeled in the context of fault rupture-soil-foundation interaction (FR-SFI) in which a fault rupture surface interacts with a foundation located atop the soil. Parametric analyses with different void ratio distributions and foundations having different contact pressures and positions provide insight into the influence of soil density on FR-SFI mechanisms. Fault rupture in nature also rarely occurs in homogeneous soil deposits. Thus, free-field surface fault rupture is modeled with alternating layers of loose and dense soils of varying thickness to better understand how fault rupture propagation behavior differs in homogeneous and inhomogeneous soils. Simulations with layered soil deposits are shown to capture features of free-field surface fault rupture that are more consistent with observations made through field reconnaissance activities than simulations with homogeneous soil deposits.