Geosystems often experience numerous loading cycles. Plastic strain accumulation during repetitive mechanical loads can lead to shear shakedown or continued shear ratcheting; in all cases, volumetric strains diminish as the specimen evolves towards terminal density. Previously suggested models and new functions are identified to fit plastic strain accumulation data. All accumulation models are formulated to capture terminal density (volumetric strain) and either shakedown or ratcheting (shear strain). Repetitive vertical loading tests under zero lateral strain conditions are conducted using three different sands packed at initially low and high densities. Test results show that plastic strain accumulation for all sands and density conditions can be captured in the same dimensionless plot defined in terms of the initial relative density, terminal density, and ratio between the amplitude of the repetitive load and the initial static load. This observation allows us to advance a simple but robust procedure to estimate the maximum one-dimensional settlement that a foundation could experience if subjected to repetitive loads.