## 5 Conclusions  
In order to achieve optimal selection of stope dimension parameters in long-hole stage open stoping with the subsequent backfill mining method, a new CRITIC-GRA model was developed and illustrated for the first time in this paper in an iron mine, which innovatively integrated the stope stability, mining capacity and costs in the analysis. The key conclusions regarding the model and its application are listed as follows. The CRITIC-GRA model proposed for selecting the optimal scheme considering the effects of multi-indicators consists of four key modules: the determination of all the considered possible influential indicators; analysis on the weight values of all the considered indicators using the CRITIC method; statistical analysis on the ranging conditions of each indicator using the GRA method to obtain the grey correlation coefficient in each scheme; and calculations on the grey correlation coefficient of each preset scheme with the weight values of all the considered indicators to obtain the grey correlation degree for each scheme. The obtained grey correlation degree serves as the only quantitative criterion to evaluate the optimum out of all the preset schemes. In the process of applying the CRITIC-GRA model to optimize stope dimensions, the key influential indicators on open stoping stability, mining capacity and costs consist of the safety indicators including stability probability for the side walls and the roof via the updated Mathews graph method, the maximum displacement, plastic zones volume and maximum principal stress via FLAC3D simulations, and the economic indicators including the mining costs and stope production capacity adopted in the mining design and practically verified in the mine operations. In the model illustration of an iron mine, the proposed CRITIC-GRA was firstly used to analyze the stability conditions of the open stope. The primary influence on stope wall stability is attributed to stope height, followed by stope length and width. The roof stability is primarily influenced by stope width, with stope length and height playing secondary roles. With the given rockmass quality in the illustrated iron mine, when the stope length exceeds 48 m, the double stage open stope with a 15 m width shows a better overall stability than the single stage open stope with a 20 m width. The overall stability of the open stope can be improved instead of reduced to enlarge the single stage stope height of 60 m to a double stage height of 120 m by reducing the stope width from 20 m to 15 m, which can significantly increase the mineable ore amount and improve the stope safety. The proposed CRITIC-GRA was employed to optimize the stope dimensions considering the stope safety and economic indicators synchronously in the demonstration iron mine. The objectively calculated weight values assigned to the economic indexes surpassed those of safety indexes, indicating that the economic factors of open stope within the preset schemes exerted a more pronounced influence on the integrated analysis and optimal selection of varying stope dimensions, which were mostly ignored in the previous analysis on stope dimension optimization. Discussions on the stope dimension optimization lose much of their value if the economic indicators are not considered along with the stability conditions. After applying the CRITIC-GRA model to the iron mine for an integrated evaluation of open stope stability, mining capacity and costs, scheme No. 10 with the stope length of \(L=50\) m, width of \(W=15\) m and height of \(H=120\) m was objectively identified as the optimal stope dimension among all the preset 20 schemes. Based on the illustration and verification of the proposed model in the mine, the proposed CRITIC-GRA model offers a dependable reference tool for determining the optimal stope dimensions in similar underground mines, considering multiple factors of designed dimension schemes, rockmass quality and technical and economic indicators of stope mining.