Understanding subsurface conditions is critical to creating and maintaining resilient infrastructure systems, such as dams and levees. Seismic geophysical tools can be very effective for site characterization of these structures as they directly measure the elastic moduli and can provide insight into both the soil properties and groundwater conditions. Full waveform inversion (FWI) is one processing option for seismic geophysics that seeks to overcome some of the limitations in the traditional approaches by using the full time-domain recording of the wavefield to develop 2D or 3D profiles of shear wave velocity. In addition to providing characterization data, FWI can also potentially be used as a monitoring tool for dams and levees to assess how elastic moduli are changing with time and to infer how these changes might relate to changes in the hydromechanical properties of the soil. This study seeks to explore the use of seismic FWI as both a characterization and monitoring tool through numerical simulations of seismic surveys on a hypothetical levee with a low velocity anomaly in the foundation. The simulations are used to assess both the spatial resolution and the ability of the simulations to detect changes in properties that might be related to softening of the foundation or development of internal erosion failure modes. The findings from the study will be used to highlight potential benefits and challenges to using seismic FWI for characterization and monitoring of dams and levees.