Abstract: Underground concealed goafs is prone to surface collapse and other problems. The stability of goaf is related to the safety of opencast mining. It is of great significance to the safety assessment of goaf to determine the critical roof thickness of goaf. The critical roof thickness of goaf is associated with multi factors such as the geometric parameters of goaf and the physical and mechanical parameters of rock mass. Through dimensional analysis， a dimensionless expression was established， the dimensionless parameters affecting the critical roof thickness were obtained. Based on this theory， numerical models were established and analyzed by CDEM numerical method.A two-dimensional numerical model of the mining area was established，through changing the geometric parameters of the mining area and the physical and mechanical parameters of the rock mass， calculating the safety coefficient of the roof of the mining area，so as to study the influence law of the above factors on the stability of mining area， and identify the main influencing factors affecting the safety coefficient of the roof. Two-dimensional models and three-dimensional models were established， the relationship between the dimensionless critical height and dimensionless strength in the dimensionless expression was obtained， and the relationship expression of the response was obtained by fitting with exponential function. The study results showed that: elastic modulus and Poisson's ratio have little effect on critical roof thickness， and the height of the extraction zone has no effect on the critical roof thickness； cohesion has the greatest effect on the safety coefficient of the extraction zone， followed by the span of the extraction zone， the internal friction angle of the rock mass and the density of rock mass； there is an exponential decay relationship between the dimensionless height and the dimensionless strength of goaf.

Key words: goaf, roof thickness, dimensional analysis, numerical simulation