Geogrids are often used in the aggregate cushion of the composite foundation to limit the lateral displacement and reduce the differential deformation. It depends on the interaction between geogrids and aggregate particles. In this study, a series of large-size pull-out tests was performed on biaxial and triaxial geogrids embedded in aggregates with three particle-size gradations. The test results showed that higher normal stress, better gradation and more suitable aggregate particle sizes yielded the increase of the pull-out resistance. The classic punching-shear failure model was proven to be valid for explaining the shear effect between transverse ribs of biaxial geogrids and the aggregate layer during the pull-out process. The bearing resistance of oblique ribs of triaxial geogrids can also be calculated based on this theory, as long as the effective length of the oblique rib is calculated in a reasonable manner. Furthermore, an empirical method was proposed to calculate the peak pull-out resistance of the extruded geogrid embedded in the aggregate considering the sizes of apertures and aggregates, and interlock effect. The concept of key particles was proposed in this paper to measure how well the apertures of geogrids match the size of the particles. This may help designers choose the type of geogrids and improve the reinforcement effect.