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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 anal-ysed 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 frac-ture 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 cur-vature 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.