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In engineering, the method of charts can provide a convenient query for specific engineering problems. To provide the basis for the potential hazard evaluation and rational governance of the goaf, it is necessary to study the quantitative evaluation for the range of goaf roof caving. Undoubtedly, the charts used to visually query the caving range can simplify the workload of the quantitative evaluation. Therefore, the methods of dimensional analysis, numerical simulation, and linear interpolation are introduced to study the dimensionless charts for predicting the caving range. The dimensionless analysis is used to establish the fuzzy function relationship among the influence factors of the goaf roof caving, and the numerical simulation is used to calculate the dimensionless groups in the fuzzy function. Using the linear interpolation, the dimensionless charts in this work can predict the range of goaf roof caving under more working conditions. The results show that the characteristics of the goaf roof caving corresponding to the dimensionless curves are consistent with the actual situation. With the continuous increase of the goaf span l, the dimensionless curves of the caving range experience zero growth, rapid growth, and steady growth. The growth degree varies with the fracture spacing S. Especially in the zero growth phase, the duration of the relatively stable state in the overlying strata of the goaf increases with the increase of fracture spacing S. Moreover, based on the case study of Shirengou Iron Mine, the dimensionless charts obtained in this work can predict the range of goaf roof caving under different working conditions, which indicates the findings of this study have certain guiding significance to the treatment of the goaf.

Underground mining activities make the fractures in the natural rock mass develop randomly. The elastic modulus of the fractured rock mass Em is changed with the redistribution and development of the fractures. An equivalent model of fractured rock mass is structured to represent the hydraulic conductivity and the rock mass strain because of the continuum theory. Dimensional analysis is very useful to build relationship of the parameters in complex physical phenomena. Based on the engineering phenomenon of groundwater flowing into the goaf along the fracture in the rock mass, a fuzzy expression among parameters such as the parameter Em, the seepage flow Q, and the exposed area of the goaf A is obtained using dimensionless analysis. To calculate the parameter Em, the fuzzy relationship is then characterized by Darcy’s law and numerical simulation. Under the scripting environment of Python, an automated program to realize the numerical simulation of all scenarios is established, which also provides convenience for drawing the dimensionless flux charts. The results show that the parameter Em can be calculated by the dimensional analysis coupled with numerical simulation. In addition, the parameter Em decreases with the increase of the parameter Q, and the integrity of rock mass is also worse. Finally, a mine example is used to verify the feasibility of the method.