# Strength and Deformation of Pillars during Mining in the Shaft Pillar
## 4 Discussion  
The effect of the slenderness ratio on the bearing capacity of pillars has been studied by many researchers. Some have reached conclusions analogous to those drawn from our measurements. For example, in [25], it is stated that at a w/h ratio >5, the friction between the pillar and the surrounding rocks causes the pillars to become unbreakable. The dependence of the bearing capacity of the pillar on the slenderness ratio is discussed in [17; 26]. In order to determine the bearing capacity of pillars, the works mentioned above establish the following relationship:  
\[\sigma_{\mathrm{s}}=k\;h^{a}w^{b} \tag{8}\]  
where \(k\) is the strength determined in situ on a cubic block with 1 m edges, h is the pillar height, \(w\) is the pillar width, and \(a\) and \(b\) are experimental constants. The following parameters were determined for the South African coal: \(\sigma_{\mathrm{s}}=7.2\) MPa, \(a=-0.66\), and \(b=0.46\). For the pillars at the CSM Mine with \(h=3\) m and \(w=25\) m, the Equation (8) \(\sigma_{\mathrm{s}}\)= 15.3 MPa applies. Since at that mine the geostatic stress is about 20 MPa and the pillars showed no instability, this seam must be much stronger than the South African coal. Based on Equation (8), we have calculated that the load capacities of the pillars for our observed range of slenderness ratio \(t\) are 1 to 8.33. The results are shown in the graph in Figure 7.  
Relationship (8) is a power function; therefore, the power regression fully fits the calculated values. The bearing capacity of the pillars as a function of the slenderness ratio according to this calculation has the following form:  
\[\sigma_{\mathrm{s}}=6.4509\;t^{-0.46} \tag{9}\]  
According to this calculation, the bearing capacity of the pillars at a slenderness ratio of 8.33 is 2.65-times higher than at a slenderness ratio of 1. Our measurements have shown that the ratio of the strength of coal samples at a slenderness ratio of 8.33 and a slenderness ratio of 1 is 8.7 and 8.0, according to the relationship (2) and (3), respectively. This implies that it is appropriate to use relationship (8) or (9) for slenderness ratios closer to 1. Pillars  
Figure 6: Typical example of a deformation diagram at a low slenderness ratio (t = 6.6). with very high slenderness ratios are rare. For Indian coal conditions, the bearing capacity of pillars has been determined from extensive measurements [27] using the relationship  
\[\sigma_{s}=0.27\sigma_{c}h^{-0.86}w^{0.5} \tag{10}\]  
where \(\sigma_{c}\) is the uniaxial compressive strength determined on a 25 mm edge cubic specimen. If our measurements on 70 mm edge cubic specimens yielded a compressive strength of 11.4 MPa, and we would assume that we would measure a strength of 20 MPa on 25 mm edge specimens, then for the dimensions of the pillars at the CSM Mine \(\sigma_{s}=10.5\) MPa, it is an even smaller increase than seen in the previous South African coal pillars for evaluation (9). From relationship (10), the load capacity ratio of the pillars at a slenderness ratio of 8.33 and a slenderness ratio of 1 is 1.94. This is an even smaller increase than that seen in the previous evaluation of South African coal pillars. Another study on the effect of the Indian coal slenderness ratio on the resulting bearing capacity [28] found that the ratio of bearing capacity of pillars at the slenderness ratio of 9.1 and the slenderness ratio of 1 is 3.55. There are many relationships that can be used for calculating the load capacity of pillars depending on their slenderness. The publication [29] evaluates 12 formulas for this calculation. Only three formulas, according to [19; 30; 31], show a steeper increase in bearing capacity with an increasing w/h ratio. The larger scatter of measured values at the same slenderness ratio in the results in Figure 3 is due to the presence of more or fewer discontinuities, which were often macroscopically noticeable on the test specimens. These discontinuities may be original, created by geological processes during the formation of the seam.