The ultimately exposed roof area (UERA) of goaf is crucial to the safety and economics of underground mining. The prediction models do not consider the mechanical weakness of rock mass and ignore the influence of the joint damage factor, causing a large predicted exposure area with a high roof falling risk. This work adopted joint damage factor to derive a new UERA prediction model. The relationships between the UERA (S) and the span ratio (m), the density (λ) and the diameter of fracture (d) were analysed by the new prediction model. The results showed that the exposed area S and the span ratio m have a U-shaped curve relationship. The S decreases with the increase of m and then increases when m is beyond 2. The exposed roof area S is in an inversely proportional power-law relationship with the fracture surface density λ, and the curvature of the S-λ relationship curve decreases when d = 0.5 and λ > 7, and S is close to 0. There is a negative correlation between S and the fracture surface diameter d, the curvature of the S-d curve decreases with the increase of d and λ, and the variation rate increases first and then decreases with the increase of d; when λ = 0.5 and d > 9, S is close to 0. The predicted values of the UERA prediction model are 119.3, 112.8, and 114.6 m² with different joint damage parameters, which are slightly smaller than the actual critical exposure area of a roof (S = 120 m²). The case study shows that the alternative prediction model is reasonable and acceptable and provides new theoretical support for the underground mining safety of sedimentary bauxite ore.

采空区的最终裸露屋顶面积（UERA）对于地下采矿的安全性和经济性至关重要。预测模型没有考虑岩体的机械弱点，并且忽略了节理破坏因素的影响，从而导致较大的预测暴露区域，并具有很高的冒顶风险。这项工作采用联合损伤因子来推导新的UERA预测模型。通过新的预测模型分析了UERA（S）与跨距比（m），密度（λ）和断裂直径（d）之间的关系。结果表明，曝光面积S和跨度比m具有U形曲线关系。在小号随着m的增加而减小，然后当m大于2时增加。当d  =时，裸露的屋顶面积S与断口表面密度λ成反比的幂律关系，并且S - λ关系曲线的曲率减小。0.5和λ  > 7，和小号接近于0之间有一个负相关小号和断裂表面直径d，所述的曲率小号- d与的增大而减小的曲线d和λ变异率随d的增大先增大后减小; 当λ  = 0.5且d  > 9时，S接近0。具有不同关节损伤参数的UERA预测模型的预测值为119.3、112.8和114.6 m ²，这些值略小于a的实际临界暴露区域屋顶（S  = 120 m ²）。实例研究表明，该替代预测模型是合理可行的，为沉积铝土矿的地下开采安全提供了新的理论依据。