Study on a Quantitative Evaluation Method of Goaf Instability Risk of Phosphate Deposits in Layered Rock Mass

Goaf instability accidents such as roof falling, rib spalling, or pillar spalling often occur during the room-pillar mining process in layered phosphate deposits, severely affecting mine production safety. Considering that the spatial variability of rock mass mechanical parameters is rarely incorporated into goaf instability analysis methods, a database for rock mass matrix cohesion (c) and internal friction angle (j) is first established in the Shanshuya phosphate deposit using the displacement inversion method. Then, the spatial variability characteristic parameters of c and j are fitted based on geostatistical principles. Random fields are constructed using the Karhunen–Loeve (K–L) series expansion method and assigned to the FLAC3D grid model through element traversal to represent the autocorrelation, cross-correlation, and non-Gaussian properties of c and j during numerical calculations. The limit state equation for rock mass failure is then established, using layered rock mass’s failure approach index (FAI) as the evaluation index. The Hermite random polynomial coefficients between the input field of c and j and the output field of the FAI are solved by the probability collocation method, establishing an explicit function expression between the probability collocation point and the FAI. Finally, the FAI for each element is calculated using the cross-correlation standard random variables instead of the probabilistic collocation points. Hence, the element failure probability of the phosphate mine goaf is determined by the Monte Carlo method, which reveals a quantitative evaluation of the goaf instability risk. The results showed that the random field assigned to the FLAC3D grid model effectively characterizes the spatial variability of rock mass mechanical parameters. The high instability risk area of the goaf (failure probability ≥ 70%) is located in the middle of the pillar within 2 meters, consistent with the actual pillar failure location and depth. Compared to conventional numerical calculations, the mechanical parameters of layered rock mass in this study exhibit objective spatial variability characteristics such as autocorrelation, cross-correlation, and non-Gaussian properties, and the calculated failure probability achieves a more specific and comprehensive quantitative evaluation of the instability risk of phosphate mine goaf. This addresses the difficulty in determining whether the phosphate mine goaf is unstable due to the varying distribution of maximum displacement, maximum and minimum principal stresses, and the FAI. The research results can provide a technical reference for stability analysis and support optimization of similar underground engineering projects in layered rock mass. © 2024 Sichuan University. All rights reserved.