## 1 Introduction
Figure 1: Typical excavating and filling sequence of (**a**) single stage and (**b**) double stage open stoping with subsequent backfill mining method. Some analytical methods based on elasticity theoretical models can also be used for stability analysis of excavated slopes. For example, [PERSON] et al. [10] used the conformal mapping method to investigate the surface shear stress distributions as well as the maximum and minimum principal stress under different in situ rock stress conditions. The results can be used to assess the stability of surrounding rockmass around stope voids in different exposure sizes. [PERSON] et al. [11] applied the complex variable function to calculate a closed-form elastic solution of the stresses and displacements of homogeneous isotropic surrounding rock, and then determined the stress distribution and concentration area of surrounding rock with different excavation sizes. Numerical modeling is a widely used and cost-effective method for investigating the stability of excavated slopes affected by various influential parameters. [PERSON] et al. [12] used ABAQUS to simulate the stope stability affected by initial and mining-induced stress conditions. [PERSON] et al. [13] applied the variability and stochasticity of the rock parameters to a FLAC model and constructed a probabilistic model for predicting the stability of practical slopes under stochastic characteristics of the surrounding rock. [PERSON] et al. [14] built up a numerical simulation method with FLAC3D to assess the influences of stope dimension parameters generated using Monte-Carlo statistics on the failure probability of excavated stope voids. Considering that the stability of excavated slopes is affected by various uncertainties, including stope sizes, physical and mechanical properties of rockmass and backfill, stress conditions and excavating processes, etc., multi-factors evaluation methods have been increasingly employed as a new approach to analyze and optimize stope dimensions [15; 16; 17]. [PERSON] et al. [18] combined a set theory model in fuzzy mathematics with a hierarchical analysis method to select appropriate stope size parameters. [PERSON] et al. [19] developed the CRITIC-TOPSIS (criteria importance through inter-criteria correlation and technique for order preference by similarity to ideal solution) evaluation model to optimize stope parameters and investigate the effect of mining depth. In summary, empirical chart methods, analytical calculation methods and numerical simulation methods have been successively used for the stability analysis and dimension optimization of excavated slopes. However, the outcomes of safety indexes and stability conditions with the above three methods are usually independent of each other, which make it difficult for the designers or managers of a specific mine to make a final decision on the optimized stope sizes with uncoordinated results. More importantly, economic indicators including production capacity and mining costs of an excavated stope should be considered simultaneously to achieve an optimized stope size, since the expectation of profit is the only excuse to continue mining. Although the multi-factors evaluation methods have been applied on the stope dimension optimization, the influences of economic parameters are mostly neglected on the selection of stope size parameters in previous published papers. There are currently no reports for the stope dimension optimization using quantitative analysis methods that integrate the economic indicators, safety indexes and stability conditions. To fill the gap, this paper proposes a new CRITIC-GRA (criteria importance through inter-criteria correlation and grey relation analysis) evaluation method for the optimization of stope dimension parameters considering the safety indexes and stability conditions of the long-hole stage open stoping mining, together with the economic indicators including stope production capacity and costs.