## 2 Newly Proposed Evaluation Method and Analysis Procedure  
The Mathews stability graph method is supposed to be the earliest published empirical method for open stoping stability analysis with the preset schemes of different stope sizes, determined mainly by comparing the Stability Index \(M\) with the Shape Factor \(S\). The Stability Index \(M\) represents the ability of surrounding rockmass of stope void to maintain unsupported self-stability under the classified rockmass quality grade and stress condition. The Shape Factor \(S\) is the hydraulic radius, calculated from the area and perimeter of the exposed walls or roof around the excavated stope void. When the Stability Index \(M\) is greater than the Shape Factor \(S\), the Mathews stability graph method indicates the stable state of the side walls or roof around the stope void. The calculation method of Stability Index \(M\) is shown in Equation (1). \[M=2.39e^{0.55\ln N} \tag{1}\]  
where, \(N\) is the rockmass quality index for the side walls or roof of the excavated stope void which can be calculated by Equation (3). The calculation method of Shape Factor \(S\) is shown in Equation (2). \[S=D/P \tag{2}\]  
where, \(D\) is the area of the exposed planes and \(P\) is the corresponding perimeter. For the shape factor of the side walls around the excavated stope void, \(D\) and \(P\) are calculated with the height \(H\) and length \(L\) of the stope. And for the shape factor of the stope roof, \(D\) and \(P\) are calculated with the stope width \(W\) and length \(L\). \[N=Q^{\prime}\times A\times B\times C \tag{3}\]  
where, \(Q^{\prime}\) is the modified \(Q\) value based on the rockmass quality rating system proposed by [PERSON] (1975); \(A\) is the stress coefficient of the rockmass; \(B\) is the adjustment coefficient for the occurrence of structural planes within the rockmass; and \(C\) is the adjustment coefficient of gravity. The tunneling quality index, also known as the \(Q\) system, is a tunneling data-based empirical classification system for surrounding rockmass that was presented by [PERSON]. The system categorizes the rockmass into nine classes and the \(Q\) value can be calculated by Equation (4). \[Q=\frac{RQD}{J_{n}}\times\frac{J_{r}}{J_{a}}\times\frac{J_{w}}{SRF} \tag{4}\]  
where, \(RQD\) is the rock quality designation, determined from the ratio of total length of the cored rock sample over 10 cm to the length of the whole core drilling, \(J_{n}\) is the number of joint sets, \(J_{r}\) is the roughness of the most unfavorable joint or discontinuity, \(J_{a}\) is the degree of alteration or filling along the weakest joint, \(J_{w}\) is the water inflow, and \(SRF\) is the stress condition given as the stress reduction factor, composed of loosening load in the case of shear zones and clay bearing rock, rock stress in competent rock, and squeezing and swelling loads in plastic incompetent rock. The value of \(Q^{\prime}\) equals to the \(Q\) value when \(J_{w}/SRF=1\) in the \(Q\) classification system. [PERSON] et al. further updated the Mathews stability graph by using a logit model to calculate the probability of stope stability instead of a fixed value, which is more reasonable for describing the safety condition of a stope void surrounded by practical rockmass with uncertainty and heterogeneity. The evaluated stable probability \(f(z)\) of the open stoping is shown in Equation (5). \[f(z)=1/(1+e^{-z}) \tag{5}\]  
\[z=2.9603-1.4427\ln S+0.7928\ln N \tag{6}\]The Mathews stability graph is widely used for stope stability analysis and dimension optimization [21; 22; 23]. In addition, to further investigate the stability conditions of the excavated stope voids, numerical simulations of the same slope are usually carried out to provide a supplementary validation against the quickly obtained results via the empirical stability graph.