Karst collapse has the characteristics of abruptness and concealment, which poses significant threats to infrastructure stability. To study the deformation control of geogrid-reinforced karst foundations, an adjustable-amplitude collapsible stratum simulation device was developed. Indoor scale model tests were conducted on both reinforced and unreinforced cases under various loading conditions to investigate surface settlement and earth pressure. Digital Image Correlation (DIC) was employed to capture the deformation characteristics during the collapse process, and complementary numerical simulations were performed to explored reinforcement mechanisms and anchorage length effects. The results show significant displacement differences between collapsed and stable area, along with soil stress redistribution after collapse. Reinforcement effectively reduced surface settlement by 61.5%, while during the collapse process, the soil arching effect preceded the membrane tension effect. Numerical simulations indicate that the influence boundary is affected by collapse, expanding with increasing collapse width and amplitude. Among the three reinforcement configurations studied, the upper short and lower long reinforcement method demonstrated the most effective collapse control. This study provides valuable insights for mitigating foundation differential settlement in karst areas.