A model was developed to predict roof fractures in coal mining, based on how the roof breaks during mining. The model uses fracture mechanics theory to understand how cracks in the roof grow and how supports can resist them. By studying a coal mine in Shanxi province, researchers found that the support resistance is related to the length of roof fractures. They also discovered that the load on the strata above is linked to the ratio of crack length to roof thickness. The study showed that the support system can handle the weight of the overlying rock in mining thick but shallow coal seams. The model's predictions were confirmed by on-site experiments, showing that the support system works well in practice.