## 5 Analysis of Factors Affecting Bearing Capacity of Inclined Pillar
It can be seen that the change of dip angle is the reason for the transformation between compressive stress and shear stress on the pillar, which shows that in this case, the bearing capacity of the pillar is controlled by the dip angle. The larger the dip angle, the smaller the pillar bearing capacity. The curve arrow \(\overset{\rightarrow}{CF}\) represents the stress path controlled by the in-situ stress ratio when the in-situ stress ratio is less than 1 (\(k<1.0\)); with the increase of in-situ stress ratio, the loading condition of the pillar converts to compression from compression-shear loading. The shear stress component on the pillar decreases and the compressive stress increases. Considering that the ore-body material has the characteristics of compressive resistance and not shear resistance, the risk of pillar instability is small, and the ability of pillar resistance to external load is enhanced. When the in-situ stress ratio is more than (\(k>1.0\)), the direction of the shear load changes; with the increase of the in-situ stress ratio, the compressive stress and shear stress on the pillar increase. The generalized Mohr circle center gradually moves below the stress axis \(\sigma\) and gradually approaches the strength envelope; thus, it is easier for the pillar to reach the limit equilibrium state, and the bearing capacity of the pillar is reduced. It should be noted that when the dip angle is small, the higher the in-situ stress ratio, the higher the shear stress concentration on the pillar, which is bound to increase the risk of pillar failure. To sum up, the changes of area extraction ratio, inclination angle, and in-situ stress ratio change the stress state of the pillar and have a weakening effect on the stability of the pillar. As a result of this weakening effect, the bearing capacity of the pillar decreases, and the pillar gradually evolves from a stable to an unstable state. Specifically, the area extraction ratio changes the total stress, the inclination angle changes the stress property (from compressive stress to shear stress), and the in-situ stress ratio changes the total load of the pillar as well as the property of stress. These changes develop in a direction that is not conducive to the stability of the pillar, resulting in a decrease in the bearing capacity of the pillar. Therefore, the stress evolution path can qualitatively judge the stability of the pillar. ### Stress Path Effect on the Bearing Capacity of Pillar  
The effect of the pre-mining stress state and dip angle on pillar stability is reflected in the _CFSL_. The strength characteristics of the inclined pillar are revealed by analyzing the relationship between the _CFSL_ and pre-mining stress state and inclination angle. In general, the range of dip angle is from 0\({}^{\circ}\) to 90\({}^{\circ}\), but there is no fixed formula to calculate the in-situ stress ratio. The most effective method to determine its value is an in-situ stress measurement. In the results of in-situ stress measurements around the world, [PERSON] and [PERSON] [8] summed up the measured range of the in-situ stress. In-situ stress ratios are bound on the lower side by \(k=0.3\), while the upper bound is defined by the following expression:  
\[k=0.3+\frac{1500}{H} \tag{25}\]  
where \(H\) is the depth below the ground surface in meters. At shallow depth, values of \(k\) vary widely and are frequently much greater than unity; at increasing depth, the variability of the ratio decreases, and the upper bound tends towards unity. When \(H\) is from 0 to 1000 m, the horizontal stress changes greatly, \(k\)\(\in\)[0.3, 3.5]; when \(H\) is greater than 1000 m, \(k\)\(\in\)[0.3, 1.0].