# Strength and Deformation of Pillars during Mining in the Shaft Pillar
## 4 Discussion
However, they may also be due to the overpressure mentioned above in the sides of the mine from which the samples were taken. The increase in compressive strength at the lower slenderness ratio is caused by the fact that the inside of the test specimen cannot be transversely reshaped due to friction at the contact surfaces. Moreover, a volumetric state of tension inside the test specimen increases the resulting compressive strength. The extent of the test specimen in the volumetric state  
Figure 7: Dependence of pillar bearing capacity on slenderness ratio for South African coal according to the Relationship (8). of tension at higher slenderness ratios is determined in various ways. For example, [3] determines this range by the appearance of the compressive surface of the test specimen after the compression test. We loaded the test specimens with a slenderness ratio of 6-8 after the ultimate strength was reached so that the final force was about 2-3-times higher than the force when the ultimate strength was reached. The part of the test specimen that was in the bulk state of tension was further compacted by the high loading, and the original height of the test specimen was reduced by up to 38% at the maximum applied force of almost 1000 kN. After the test, the compacted residue of the test specimen remained intact and could be handled manually. This strengthened portion of the specimen represents approximately the region where the volumetric stresses occur. An example of this strengthened residue is shown in Figure 8.  
These compact low slenderness ratio remnants of the test specimen were weighed after the test. Their \(\mathrm{G_{v}}\) weight to \(\mathrm{G_{o}}\) pre-test weight ratio ranged from 0.45 to 0.61, with an average of 0.55. These values were found for a w/h ratio ranging from 6.25 to 7.69. The graphical dependence of the \(\mathrm{G_{v}}/\mathrm{G_{o}}\) ratio on the slenderness ratio is shown in Figure 9.  
Figure 8: Example of strengthened core of test specimen residue with slenderness ratio 6.25. Figure 9: Ratio of the hardened part of the sample to the original sample as a function of t.  
The linear regression relationship with the index of determination R\({}^{2}\) = 0.89 has the form  
Figure 7.0  
For the pillars used with a \(\rm w/h\) ratio of 8.33, this equation yields \(\rm G_{v}/G_{0}=0.72\). For this representation of the volumetric state of stress in a 25 m wide and 3 m high pillar, the loosening of the pillars would occur to a depth of 1.9 m. In the case under consideration, this value for the loosening of the pillars could not be verified because, for safety reasons, the sides of the chambers were reinforced with roof bolts. As the slenderness ratio of the pillars decreases, the impact of more discontinuities in a larger volume on the resulting bearing capacity of the pillars changes. Even though the entire column is interspersed with a large number of discontinuities, the majority of the column volume is in a bulk state of tension, and the discontinuities contained within it do not contribute as much to the reduction in the column capacity. It can be seen clearly in the strengthened low-slederness-ratio residue of the test specimen after compression testing. The original discontinuities in this part of the test specimen have been compressed via the volumetric compression, giving the test specimen a higher strength. The laboratory-determined compressive strength is influenced by the amount of friction on the compression surfaces. Many papers [3; 4; 5; 32; 33; 34; 35; 36; 37] have addressed this issue. These works clearly show that lower friction between the test specimen and the loading mechanism also lowers compressive strength. In the laboratory tests, we used very smooth steel jaws, which showed a coefficient of friction of 0.45 with the coal samples. The pillars in mining conditions have sandstone in the overburden and siltstone in the bedrock. Thus, the coefficient of friction between the pillar and the surrounding rocks will definitely be higher than in the laboratory tests.