Geogrid reinforcement has been extensively used over the past few decades to enhance the stability and load carrying capacity of different geomaterials. Understanding soil-geogrid interaction is essential for the analysis and design of geogrid-reinforced structures. A three-dimensional discrete element model that is capable of capturing the response of granular material with geogrid inclusion is developed in this study. The 3D shape of the crushed limestone is modelled by tracing the surface area of a typical particle and fitting a number of bonded spheres into the generated surface. Model calibration is performed using triaxial and direct shear tests to determine the microparameters that allow for the stress-strain behavior of the backfill material to be replicated. The model is validated using experimental data and applied to simulate a series of crushed limestone reinforced with geogrid and subjected to surface loading. The analysis allows for the explicit geometry of the geogrid and the discontinuous nature of the soil to be captured. This study suggests that modeling the 3D geogrid geometry is important to accurately capture the geogrid response under both confined and unconfined conditions. Accounting for the particle shape in the analysis can significantly enhance the predicted response of the geogrid-soil system. The calculated response confirms the observed behaviour of reinforced sands and explains the increase in load carrying capacity of reinforced systems used in different geotechnical engineering applications. The proposed modelling approach has proven to be efficient in modelling this class of problems and can be adapted for other reinforced soil applications.